%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 7.29s 1.64s
% Output : Proof 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 24 unt; 0 def)
% Number of atoms : 120 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 82 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 14 ( 3 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 : 129 ( 76 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( qtd0(f(B_0),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_10) ).
fof(f9_nnf,plain,
! [A_0,B_0] :
( qtd0(f(B_0),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A_0,B_0] :
( qtd0(f(B_0),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( qtd0(f(X1),s(s(s(qtd1))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(qtd1))))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(qtd0(f(X0),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,qtd0(f(X1),s(s(s(qtd1)))),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f3,axiom,
qtd0(f(B_0),s(s(s(s(qtd1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_04) ).
fof(f3_nnf,plain,
! [B_0] : qtd0(f(B_0),s(s(s(s(qtd1))))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B_0] : qtd0(f(B_0),s(s(s(s(qtd1))))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
qtd0(f(X0),s(s(s(s(qtd1))))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
qtd0(f(X0),s(s(s(s(qtd1))))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f4,axiom,
qtd0(f(B),s(s(s(s(s(qtd1)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_05) ).
fof(f4_nnf,plain,
! [B] : qtd0(f(B),s(s(s(s(s(qtd1)))))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B] : qtd0(f(B),s(s(s(s(s(qtd1)))))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
qtd0(f(X0),s(s(s(s(s(qtd1)))))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
qtd0(f(X0),s(s(s(s(s(qtd1)))))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1,plain,
qtd0(f(V0),s(s(s(qtd1)))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi2,hi3]) ).
cnf(f11,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_12) ).
fof(f11_nnf,plain,
! [A_0,B_0,A_1,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A_0,B_0,A_1,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X3)),s(s(qtd1)))
| ~ qtd0(f(X2),s(s(s(qtd1))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(qtd1))))) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,axiom,
ifeq(qtd0(f(X0),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X3)),s(s(qtd1))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h2,plain,
qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),V0)),s(s(qtd1))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi2,hi3,h1]) ).
cnf(f8,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(qtd1))
| ~ qtd0(f(A_2),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_09) ).
fof(f8_nnf,plain,
! [A_0,B_0,A_1,A_2,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(qtd1))
| ~ qtd0(f(A_2),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A_0,B_0,A_1,A_2,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),s(qtd1))
| ~ qtd0(f(A_2),s(s(qtd1)))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1))))) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X4)),s(qtd1))
| ~ qtd0(f(X3),s(s(qtd1)))
| ~ qtd0(f(X2),s(s(s(qtd1))))
| ~ qtd0(f(X1),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X0),s(s(s(s(qtd1))))) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(qtd0(f(X0),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X1),s(s(s(s(s(qtd1)))))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,ifeq(qtd0(f(X3),s(s(qtd1))),true,qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X4)),s(qtd1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h4,plain,
qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),V0)),s(qtd1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,hi3,h1,h2]) ).
cnf(f6,axiom,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),qtd1)
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_07) ).
fof(f6_nnf,plain,
! [A_2,A_0,A_1,A_3,B_0,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),qtd1)
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A_2,A_0,A_1,A_3,B_0,K] :
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),K)),qtd1)
| ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X5)),qtd1)
| ~ qtd0(f(X4),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X3),s(qtd1))
| ~ qtd0(f(X2),s(s(s(qtd1))))
| ~ qtd0(f(X1),s(s(s(s(qtd1)))))
| ~ qtd0(f(X0),s(s(qtd1))) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(qtd0(f(X0),s(s(qtd1))),true,ifeq(qtd0(f(X1),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),s(s(s(s(s(qtd1)))))),true,qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),X5)),qtd1),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h7,plain,
qtd0(f(qtd3(s(s(s(s(s(s(qtd1)))))),V0)),qtd1) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2,hi2,h1,h4,hi3]) ).
cnf(f2,axiom,
( ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_4),qtd1)
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_03) ).
fof(f2_nnf,plain,
! [A_2,A_0,A_1,A_3,A_4,B_0] :
( ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_4),qtd1)
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A_2,A_0,A_1,A_3,A_4,B_0] :
( ~ qtd0(f(B_0),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(A_4),qtd1)
| ~ qtd0(f(A_3),s(qtd1))
| ~ qtd0(f(A_1),s(s(s(qtd1))))
| ~ qtd0(f(A_0),s(s(s(s(qtd1)))))
| ~ qtd0(f(A_2),s(s(qtd1))) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ qtd0(f(X5),s(s(s(s(s(qtd1))))))
| ~ qtd0(f(X4),qtd1)
| ~ qtd0(f(X3),s(qtd1))
| ~ qtd0(f(X2),s(s(s(qtd1))))
| ~ qtd0(f(X1),s(s(s(s(qtd1)))))
| ~ qtd0(f(X0),s(s(qtd1))) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi12,axiom,
ifeq(qtd0(f(X0),s(s(qtd1))),true,ifeq(qtd0(f(X1),s(s(s(s(qtd1))))),true,ifeq(qtd0(f(X2),s(s(s(qtd1)))),true,ifeq(qtd0(f(X3),s(qtd1)),true,ifeq(qtd0(f(X4),qtd1),true,ifeq(qtd0(f(X5),s(s(s(s(s(qtd1)))))),true,false,true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi12,h2,hi2,h1,h4,h7,hi3]) ).
cnf(t48,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t48]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 03:21:27 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.29/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.29/1.64 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------