%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:48:34 PM UTC 2026
% Result : Unsatisfiable 4.16s 0.94s
% Output : Proof 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 13
% Syntax : Number of formulae : 164 ( 124 unt; 0 def)
% Number of atoms : 420 ( 115 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 518 ( 262 ~; 256 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 24 ( 4 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 740 ( 580 sgn 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,axiom,
( ~ qtd0(f(A_9),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_17) ).
fof(f16_nnf,plain,
! [A_1,A_4,A_8,B_0,A_5,A_7,A_2,A_6,A_0,A_3,A_9] :
( ~ qtd0(f(A_9),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A_1,A_4,A_8,B_0,A_5,A_7,A_2,A_6,A_0,A_3,A_9] :
( ~ qtd0(f(A_9),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ qtd0(f(X10),qtd1)
| ~ qtd0(f(X9),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X7),s(s(s(qtd1))))
| ~ qtd0(f(X6),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X5),s(s(qtd1)))
| ~ qtd0(f(X4),s(s(s(s(qtd1)))))
| ~ qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X2),s(qtd1))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t33,plain,
ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f0,axiom,
( qtd0(f(B_0),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21_01) ).
fof(f0_nnf,plain,
! [A_0,B_0] :
( qtd0(f(B_0),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A_0,B_0] :
( qtd0(f(B_0),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f8,axiom,
qtd0(f(B_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17_09) ).
fof(f8_nnf,plain,
! [B_0] : qtd0(f(B_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B_0] : qtd0(f(B_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f2,axiom,
qtd0(f(B),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11_03) ).
fof(f2_nnf,plain,
! [B] : qtd0(f(B),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : qtd0(f(B),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
qtd0(f(X0),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
qtd0(f(X0),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t6,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi8,hi2]) ).
cnf(t41,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t270,plain,
ifeq(true,true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t33,t41]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t38,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t271,plain,
ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t270,t38]) ).
cnf(h1,plain,
qtd0(f(V0),s(s(s(s(s(s(s(s(qtd1))))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi8,hi2]) ).
cnf(f13,axiom,
( qtd0(f(B_0),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_14) ).
fof(f13_nnf,plain,
! [A_0,B_0,A_1] :
( qtd0(f(B_0),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A_0,B_0,A_1] :
( qtd0(f(B_0),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( qtd0(f(X1),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(s(qtd1))))))))),true,qtd0(f(X1),s(s(s(s(s(s(s(qtd1)))))))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h3,plain,
qtd0(f(V0),s(s(s(s(s(s(s(qtd1)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi8,hi2,h1]) ).
cnf(f5,axiom,
( qtd0(f(B_0),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_06) ).
fof(f5_nnf,plain,
! [A_0,B_0,A_1,A_2] :
( qtd0(f(B_0),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A_0,B_0,A_1,A_2] :
( qtd0(f(B_0),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( qtd0(f(X1),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X3),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(qtd1)))))))))
| ~ qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(qtd1)))))))),true,qtd0(f(X1),s(s(s(s(s(s(qtd1))))))),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h5,plain,
qtd0(f(V0),s(s(s(s(s(s(qtd1))))))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi8,hi2,h1,h3]) ).
cnf(f19,axiom,
( qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15_20) ).
fof(f19_nnf,plain,
! [A_1,B_0,A_2,A_0,A_3] :
( qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A_1,B_0,A_2,A_0,A_3] :
( qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X4),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X3),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi18,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(X1),s(s(s(s(s(qtd1)))))),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t1,plain,
qtd0(f(X1),s(s(s(s(s(qtd1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h1,hi2,h3,hi8,h5]) ).
cnf(t44,plain,
qtd0(f(X1),s(s(s(s(s(qtd1)))))) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t272,plain,
ifeq(true,true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t271,t44]) ).
cnf(t273,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t272,t38]) ).
cnf(t10,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t39,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t274,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(true,true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t273,t39]) ).
cnf(t275,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t274,t38]) ).
cnf(t4,plain,
qtd0(f(X1),s(s(s(s(s(s(s(qtd1)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi8,hi2,h1]) ).
cnf(t42,plain,
qtd0(f(X1),s(s(s(s(s(s(s(qtd1)))))))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t276,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(true,true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t275,t42]) ).
cnf(t277,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t276,t38]) ).
cnf(t8,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(s(qtd1)))))))))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t40,plain,
qtd0(f(X1),s(s(s(s(s(s(s(s(s(qtd1)))))))))) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t278,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(true,true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t277,t40]) ).
cnf(t279,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t278,t38]) ).
cnf(t2,plain,
qtd0(f(X1),s(s(s(s(s(s(qtd1))))))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi8,hi2,h1,h3]) ).
cnf(t43,plain,
qtd0(f(X1),s(s(s(s(s(s(qtd1))))))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t280,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(true,true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t279,t43]) ).
cnf(t281,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X11),qtd1),true,false,true),true),true),true),true) = true,
inference(step,[status(thm)],[t280,t38]) ).
cnf(t73,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X3),s(s(qtd1))),true,ifeq(qtd0(f(X4),s(s(s(qtd1)))),true,ifeq(qtd0(f(X5),qtd1),true,false,true),true),true),true),true) = true,
inference(orient,[status(thm)],[t281]) ).
cnf(h7,plain,
qtd0(f(V0),s(s(s(s(s(qtd1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h1,hi2,h3,hi8,h5]) ).
cnf(f11,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9_12) ).
fof(f11_nnf,plain,
! [A_1,A_4,B_0,A_2,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A_1,A_4,B_0,A_2,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X6)),s(s(s(s(qtd1)))))
| ~ qtd0(f(X5),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X4),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X3),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X6)),s(s(s(s(qtd1))))),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t16,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(s(s(qtd1))))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h1,h7,hi2,h3,hi8,h5]) ).
cnf(t45,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(s(s(qtd1))))) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t74,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(true,true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,ifeq(qtd0(f(X4),qtd1),true,false,true),true),true),true),true),
inference(cp,[status(thm)],[t73,t45]) ).
cnf(t295,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,ifeq(qtd0(f(X4),qtd1),true,false,true),true),true),true),
inference(step,[status(thm)],[t74,t38]) ).
cnf(t86,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,ifeq(qtd0(f(X4),qtd1),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t295]) ).
cnf(h8,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),V0)),s(s(s(s(qtd1))))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h1,h7,hi2,h3,hi8,h5]) ).
cnf(f14,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(qtd1))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_15) ).
fof(f14_nnf,plain,
! [A_1,A_4,B_0,A_5,A_2,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(qtd1))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A_1,A_4,B_0,A_5,A_2,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(s(qtd1))))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X7)),s(s(s(qtd1))))
| ~ qtd0(f(X6),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X5),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X4),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X3),s(s(s(s(qtd1)))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X3),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X5),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X7)),s(s(s(qtd1)))),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t14,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(s(qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1,h7,hi2,h8,h3,hi8,h5]) ).
cnf(t46,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(s(qtd1)))) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t88,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(true,true,ifeq(qtd0(f(X3),qtd1),true,false,true),true),true),true),
inference(cp,[status(thm)],[t86,t46]) ).
cnf(t296,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),qtd1),true,false,true),true),true),
inference(step,[status(thm)],[t88,t38]) ).
cnf(t89,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),qtd1),true,false,true),true),true) = true,
inference(orient,[status(thm)],[t296]) ).
cnf(h10,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),V0)),s(s(s(qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1,h7,hi2,h8,h3,hi8,h5]) ).
cnf(f18,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0_19) ).
fof(f18_nnf,plain,
! [A_1,A_4,B_0,A_5,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A_1,A_4,B_0,A_5,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X8)),s(s(qtd1)))
| ~ qtd0(f(X7),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X6),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X5),s(s(s(qtd1))))
| ~ qtd0(f(X4),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X3),s(s(s(s(qtd1)))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi17,axiom,
ifeq(qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X3),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X5),s(s(s(qtd1)))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X8)),s(s(qtd1))),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t13,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(qtd1))) = true,
inference(hyper_resolution,[status(thm)],[hi17,h1,h7,hi2,h8,h3,h10,hi8,h5]) ).
cnf(t47,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(s(qtd1))) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t90,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(true,true,ifeq(qtd0(f(X2),qtd1),true,false,true),true),true),
inference(cp,[status(thm)],[t89,t47]) ).
cnf(t297,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),qtd1),true,false,true),true),
inference(step,[status(thm)],[t90,t38]) ).
cnf(t91,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),qtd1),true,false,true),true) = true,
inference(orient,[status(thm)],[t297]) ).
cnf(f10,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(qtd1))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_11) ).
fof(f10_nnf,plain,
! [A_1,A_4,B_0,A_5,A_7,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(qtd1))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A_1,A_4,B_0,A_5,A_7,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),s(qtd1))
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X9)),s(qtd1))
| ~ qtd0(f(X8),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X7),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X6),s(s(s(qtd1))))
| ~ qtd0(f(X5),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X4),s(s(qtd1)))
| ~ qtd0(f(X3),s(s(s(s(qtd1)))))
| ~ qtd0(f(X2),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t34,plain,
ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t234,plain,
ifeq(true,true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t34,t41]) ).
cnf(t235,plain,
ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t234,t38]) ).
cnf(t236,plain,
ifeq(true,true,ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t235,t44]) ).
cnf(t237,plain,
ifeq(qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t236,t38]) ).
cnf(t238,plain,
ifeq(true,true,ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t237,t39]) ).
cnf(t239,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X6),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t238,t38]) ).
cnf(t240,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(true,true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t239,t42]) ).
cnf(t241,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true) = true,
inference(step,[status(thm)],[t240,t38]) ).
cnf(t242,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(true,true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true),true) = true,
inference(step,[status(thm)],[t241,t40]) ).
cnf(t243,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true) = true,
inference(step,[status(thm)],[t242,t38]) ).
cnf(t244,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true),true) = true,
inference(step,[status(thm)],[t243,t43]) ).
cnf(t245,plain,
ifeq(qtd0(f(X4),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X5),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),s(qtd1)),true),true),true) = true,
inference(step,[status(thm)],[t244,t38]) ).
cnf(t61,plain,
ifeq(qtd0(f(X1),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X4)),s(qtd1)),true),true),true) = true,
inference(orient,[status(thm)],[t245]) ).
cnf(t62,plain,
true = ifeq(true,true,ifeq(qtd0(f(X1),s(s(qtd1))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),s(qtd1)),true),true),true),
inference(cp,[status(thm)],[t61,t45]) ).
cnf(t301,plain,
true = ifeq(qtd0(f(X1),s(s(qtd1))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),s(qtd1)),true),true),
inference(step,[status(thm)],[t62,t38]) ).
cnf(t96,plain,
ifeq(qtd0(f(X1),s(s(qtd1))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),s(qtd1)),true),true) = true,
inference(orient,[status(thm)],[t301]) ).
cnf(t98,plain,
true = ifeq(qtd0(f(X1),s(s(qtd1))),true,ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),s(qtd1)),true),true),
inference(cp,[status(thm)],[t96,t46]) ).
cnf(t302,plain,
true = ifeq(qtd0(f(X1),s(s(qtd1))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),s(qtd1)),true),
inference(step,[status(thm)],[t98,t38]) ).
cnf(t99,plain,
ifeq(qtd0(f(X1),s(s(qtd1))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),s(qtd1)),true) = true,
inference(orient,[status(thm)],[t302]) ).
cnf(t100,plain,
true = ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(qtd1)),true),
inference(cp,[status(thm)],[t99,t47]) ).
cnf(t303,plain,
true = qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(qtd1)),
inference(step,[status(thm)],[t100,t38]) ).
cnf(t101,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),s(qtd1)) = true,
inference(orient,[status(thm)],[t303]) ).
cnf(t102,plain,
true = ifeq(true,true,ifeq(qtd0(f(X1),qtd1),true,false,true),true),
inference(cp,[status(thm)],[t91,t101]) ).
cnf(t307,plain,
true = ifeq(qtd0(f(X1),qtd1),true,false,true),
inference(step,[status(thm)],[t102,t38]) ).
cnf(t113,plain,
ifeq(qtd0(f(X1),qtd1),true,false,true) = true,
inference(orient,[status(thm)],[t307]) ).
cnf(f21,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10_22) ).
fof(f21_nnf,plain,
! [A_1,A_4,A_8,B_0,A_5,A_7,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A_1,A_4,A_8,B_0,A_5,A_7,A_2,A_6,A_0,A_3,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),K)),qtd1)
| ~ qtd0(f(A_3),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(A_0),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(A_6),s(s(s(qtd1))))
| ~ qtd0(f(A_2),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(A_7),s(s(qtd1)))
| ~ qtd0(f(A_5),s(s(s(s(qtd1)))))
| ~ qtd0(f(B_0),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(A_8),s(qtd1))
| ~ qtd0(f(A_4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_1),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X10)),qtd1)
| ~ qtd0(f(X9),s(s(s(s(s(s(qtd1)))))))
| ~ qtd0(f(X8),s(s(s(s(s(s(s(s(s(qtd1))))))))))
| ~ qtd0(f(X7),s(s(s(qtd1))))
| ~ qtd0(f(X6),s(s(s(s(s(s(s(qtd1))))))))
| ~ qtd0(f(X5),s(s(qtd1)))
| ~ qtd0(f(X4),s(s(s(s(qtd1)))))
| ~ qtd0(f(X3),s(s(s(s(s(s(s(s(s(s(qtd1)))))))))))
| ~ qtd0(f(X2),s(qtd1))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(s(s(s(s(qtd1))))))))) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t36,plain,
ifeq(qtd0(f(X1),s(s(s(s(s(s(s(s(qtd1))))))))),true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t258,plain,
ifeq(true,true,ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t36,t41]) ).
cnf(t259,plain,
ifeq(qtd0(f(X2),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t258,t38]) ).
cnf(t260,plain,
ifeq(true,true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t259,t44]) ).
cnf(t261,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t260,t38]) ).
cnf(t262,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(true,true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t261,t39]) ).
cnf(t263,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X7),s(s(s(s(s(s(s(qtd1)))))))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t262,t38]) ).
cnf(t264,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(true,true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t263,t42]) ).
cnf(t265,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X9),s(s(s(s(s(s(s(s(s(qtd1)))))))))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t264,t38]) ).
cnf(t266,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(true,true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true),true) = true,
inference(step,[status(thm)],[t265,t40]) ).
cnf(t267,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(qtd0(f(X10),s(s(s(s(s(s(qtd1))))))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true) = true,
inference(step,[status(thm)],[t266,t38]) ).
cnf(t268,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true),true) = true,
inference(step,[status(thm)],[t267,t43]) ).
cnf(t269,plain,
ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X5),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X6),s(s(qtd1))),true,ifeq(qtd0(f(X8),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X11)),qtd1),true),true),true),true) = true,
inference(step,[status(thm)],[t268,t38]) ).
cnf(t69,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X3),s(s(qtd1))),true,ifeq(qtd0(f(X4),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X5)),qtd1),true),true),true),true) = true,
inference(orient,[status(thm)],[t269]) ).
cnf(t70,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(true,true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X4)),qtd1),true),true),true),true),
inference(cp,[status(thm)],[t69,t45]) ).
cnf(t322,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X4)),qtd1),true),true),true),
inference(step,[status(thm)],[t70,t38]) ).
cnf(t130,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(qtd0(f(X3),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X4)),qtd1),true),true),true) = true,
inference(orient,[status(thm)],[t322]) ).
cnf(t133,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),qtd1),true),true),true),
inference(cp,[status(thm)],[t130,t46]) ).
cnf(t323,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),qtd1),true),true),
inference(step,[status(thm)],[t133,t38]) ).
cnf(t134,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(qtd0(f(X2),s(s(qtd1))),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X3)),qtd1),true),true) = true,
inference(orient,[status(thm)],[t323]) ).
cnf(t136,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),qtd1),true),true),
inference(cp,[status(thm)],[t134,t47]) ).
cnf(t324,plain,
true = ifeq(qtd0(f(X1),s(qtd1)),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),qtd1),true),
inference(step,[status(thm)],[t136,t38]) ).
cnf(t137,plain,
ifeq(qtd0(f(X1),s(qtd1)),true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X2)),qtd1),true) = true,
inference(orient,[status(thm)],[t324]) ).
cnf(t138,plain,
true = ifeq(true,true,qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),qtd1),true),
inference(cp,[status(thm)],[t137,t101]) ).
cnf(t325,plain,
true = qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),qtd1),
inference(step,[status(thm)],[t138,t38]) ).
cnf(t139,plain,
qtd0(f(qtd3(s(s(s(s(s(s(s(s(s(s(s(qtd1))))))))))),X1)),qtd1) = true,
inference(orient,[status(thm)],[t325]) ).
cnf(t140,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t113,t139]) ).
cnf(t326,plain,
true = false,
inference(step,[status(thm)],[t140,t38]) ).
cnf(t142,plain,
false = true,
inference(orient,[status(thm)],[t326]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t142]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 03:18:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.16/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.16/0.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------