%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN621-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 03:35:20 PM UTC 2026
% Result : Unsatisfiable 14.10s 2.26s
% Output : Proof 14.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 43 unt; 0 def)
% Number of atoms : 79 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-4 aty)
% Number of variables : 107 ( 15 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f17,negated_conjecture,
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_18) ).
fof(f17_nnf,plain,
! [X30,X31,X32] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X30,X31,X32] :
( ~ p21(X32,X31)
| ~ p21(X30,X32)
| p21(X30,X31) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ p21(X2,X1)
| ~ p21(X0,X2)
| p21(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t22,plain,
ifeq(p21(X1,X2),true,ifeq(p21(X2,X3),true,p21(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t58,plain,
ifeq(p21(X1,X2),true,ifeq(p21(X2,X3),true,p21(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f30,negated_conjecture,
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_31) ).
fof(f30_nnf,plain,
! [X33] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X33] :
( ~ p22(X33,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X33))) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ p22(X0,f14(f11(c25,f12(c23,c26))))
| p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X0))) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t35,plain,
ifeq(p22(X1,f14(f11(c25,f12(c23,c26)))),true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t69,plain,
ifeq(p22(X1,f14(f11(c25,f12(c23,c26)))),true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,X1))),true) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(f27,negated_conjecture,
( p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18))))
| p2(X15,f3(c24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_28) ).
fof(f27_nnf,plain,
! [X15,X17,X18,X16] :
( p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18))))
| p2(X15,f3(c24)) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X15,X17,X18,X16] :
( p22(f20(X17,X15,X18,X16),f14(f11(X17,f12(X15,X18))))
| p2(X15,f3(c24)) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( p22(f20(X1,X0,X2,X3),f14(f11(X1,f12(X0,X2))))
| p2(X0,f3(c24)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t26,plain,
or(p2(X1,f3(c24)),p22(f20(X2,X1,X3,X4),f14(f11(X2,f12(X1,X3))))) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t109,plain,
or(p2(X1,f3(c24)),p22(f20(X2,X1,X3,X4),f14(f11(X2,f12(X1,X3))))) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f6,negated_conjecture,
~ p2(c23,f3(c24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_7) ).
fof(f6_nnf,plain,
~ p2(c23,f3(c24)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ p2(c23,f3(c24)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ p2(c23,f3(c24)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
p2(c23,f3(c24)) = false,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t125,plain,
p2(c23,f3(c24)) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t136,plain,
true = or(false,p22(f20(X1,c23,X2,X3),f14(f11(X1,f12(c23,X2))))),
inference(cp,[status(thm)],[t109,t125]) ).
cnf(t2,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t43,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t372,plain,
true = p22(f20(X1,c23,X2,X3),f14(f11(X1,f12(c23,X2)))),
inference(step,[status(thm)],[t136,t43]) ).
cnf(t175,plain,
p22(f20(X1,c23,X2,X3),f14(f11(X1,f12(c23,X2)))) = true,
inference(orient,[status(thm)],[t372]) ).
cnf(t179,plain,
true = ifeq(true,true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,X1)))),true),
inference(cp,[status(thm)],[t69,t175]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t394,plain,
true = p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,X1)))),
inference(step,[status(thm)],[t179,t41]) ).
cnf(t242,plain,
p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f5(f6(c27,f20(c25,c23,c26,X1)))) = true,
inference(orient,[status(thm)],[t394]) ).
cnf(t247,plain,
true = ifeq(true,true,ifeq(p21(f5(f6(c27,f20(c25,c23,c26,X1))),X2),true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),X2),true),true),
inference(cp,[status(thm)],[t58,t242]) ).
cnf(t417,plain,
true = ifeq(p21(f5(f6(c27,f20(c25,c23,c26,X1))),X2),true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),X2),true),
inference(step,[status(thm)],[t247,t41]) ).
cnf(t322,plain,
ifeq(p21(f5(f6(c27,f20(c25,c23,c26,X1))),X2),true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),X2),true) = true,
inference(orient,[status(thm)],[t417]) ).
cnf(f33,negated_conjecture,
( p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24))))))
| p2(X15,f3(c24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_34) ).
fof(f33_nnf,plain,
! [X15,X16,X17,X18] :
( p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24))))))
| p2(X15,f3(c24)) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X15,X16,X17,X18] :
( p21(f5(f6(X16,f20(X17,X15,X18,X16))),f15(f19(f11(X17,f12(X15,X18)),X16),f16(f3(f17(f18(c24))))))
| p2(X15,f3(c24)) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
( p21(f5(f6(X1,f20(X2,X0,X3,X1))),f15(f19(f11(X2,f12(X0,X3)),X1),f16(f3(f17(f18(c24))))))
| p2(X0,f3(c24)) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(t37,plain,
or(p2(X1,f3(c24)),p21(f5(f6(X2,f20(X3,X1,X4,X2))),f15(f19(f11(X3,f12(X1,X4)),X2),f16(f3(f17(f18(c24))))))) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(t108,plain,
or(p2(X1,f3(c24)),p21(f5(f6(X2,f20(X3,X1,X4,X2))),f15(f19(f11(X3,f12(X1,X4)),X2),f16(f3(f17(f18(c24))))))) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t141,plain,
true = or(false,p21(f5(f6(X1,f20(X2,c23,X3,X1))),f15(f19(f11(X2,f12(c23,X3)),X1),f16(f3(f17(f18(c24))))))),
inference(cp,[status(thm)],[t108,t125]) ).
cnf(t402,plain,
true = p21(f5(f6(X1,f20(X2,c23,X3,X1))),f15(f19(f11(X2,f12(c23,X3)),X1),f16(f3(f17(f18(c24)))))),
inference(step,[status(thm)],[t141,t43]) ).
cnf(t267,plain,
p21(f5(f6(X1,f20(X2,c23,X3,X1))),f15(f19(f11(X2,f12(c23,X3)),X1),f16(f3(f17(f18(c24)))))) = true,
inference(orient,[status(thm)],[t402]) ).
cnf(t323,plain,
true = ifeq(true,true,p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),true),
inference(cp,[status(thm)],[t322,t267]) ).
cnf(t418,plain,
true = p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(step,[status(thm)],[t323,t41]) ).
cnf(f31,negated_conjecture,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p21_32) ).
fof(f31_nnf,plain,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t34,plain,
p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) = false,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t143,plain,
p21(f5(f6(c27,f9(f11(c25,f12(c23,c26)),c28,c27))),f15(f19(f11(c25,f12(c23,c26)),c27),f16(f3(f17(f18(c24)))))) = false,
inference(orient,[status(thm)],[t34]) ).
cnf(t419,plain,
true = false,
inference(step,[status(thm)],[t418,t143]) ).
cnf(t327,plain,
false = true,
inference(orient,[status(thm)],[t419]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c31]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t327]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN621-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.40 % Computer : n004.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Fri Sep 25 01:54:51 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.10/2.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.10/2.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------