%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN587-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 03:35:15 PM UTC 2026
% Result : Unsatisfiable 20.47s 3.09s
% Output : Proof 20.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 62 unt; 0 def)
% Number of atoms : 102 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 42 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 102 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,negated_conjecture,
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_17) ).
fof(f16_nnf,plain,
! [X9,X10,X11,X12] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X9,X10,X11,X12] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p15(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p15(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t30,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,ifeq(p15(X1,X3),true,p15(X2,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t47,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,ifeq(p15(X1,X3),true,p15(X2,X4),true),true),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(f17,negated_conjecture,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_18) ).
fof(f17_nnf,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t18,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t74,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t75,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),X1),true,ifeq(p2(c20,X2),true,ifeq(true,true,p15(X1,X2),true),true),true),
inference(cp,[status(thm)],[t47,t74]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t3933,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),X1),true,ifeq(p2(c20,X2),true,p15(X1,X2),true),true),
inference(step,[status(thm)],[t75,t34]) ).
cnf(t3543,plain,
ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),X1),true,ifeq(p2(c20,X2),true,p15(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t3933]) ).
cnf(f18,negated_conjecture,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_19) ).
fof(f18_nnf,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t19,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) = false,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t113,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t3547,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21)),true,ifeq(p2(c20,c20),true,false,true),true),
inference(cp,[status(thm)],[t3543,t113]) ).
cnf(f15,negated_conjecture,
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).
fof(f15_nnf,plain,
! [X14,X15,X13] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X14,X15,X13] :
( ~ p2(X13,X15)
| ~ p2(X13,X14)
| p2(X14,X15) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t22,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t48,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f3,negated_conjecture,
p2(X13,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
! [X13] : p2(X13,X13),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X13] : p2(X13,X13),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t5,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t79,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t82,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(X2,X1),true),true),
inference(cp,[status(thm)],[t48,t79]) ).
cnf(t3604,plain,
true = ifeq(p2(X1,X2),true,p2(X2,X1),true),
inference(step,[status(thm)],[t82,t34]) ).
cnf(t481,plain,
ifeq(p2(X1,X2),true,p2(X2,X1),true) = true,
inference(orient,[status(thm)],[t3604]) ).
cnf(f19,negated_conjecture,
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_20) ).
fof(f19_nnf,plain,
! [X16,X17,X18,X19] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X16,X17,X18,X19] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p2(f4(X0,X1),f4(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t27,plain,
ifeq(p2(X1,X2),true,ifeq(p3(X3,X4),true,p2(f4(X1,X3),f4(X2,X4)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t46,plain,
ifeq(p2(X1,X2),true,ifeq(p3(X3,X4),true,p2(f4(X1,X3),f4(X2,X4)),true),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f4,negated_conjecture,
p3(c21,c19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).
fof(f4_nnf,plain,
p3(c21,c19),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p3(c21,c19),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t7,plain,
p3(c21,c19) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t64,plain,
p3(c21,c19) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t72,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(f4(X1,c21),f4(X2,c19)),true),true),
inference(cp,[status(thm)],[t46,t64]) ).
cnf(t3830,plain,
true = ifeq(p2(X1,X2),true,p2(f4(X1,c21),f4(X2,c19)),true),
inference(step,[status(thm)],[t72,t34]) ).
cnf(t2639,plain,
ifeq(p2(X1,X2),true,p2(f4(X1,c21),f4(X2,c19)),true) = true,
inference(orient,[status(thm)],[t3830]) ).
cnf(t2640,plain,
true = ifeq(true,true,p2(f4(X1,c21),f4(X1,c19)),true),
inference(cp,[status(thm)],[t2639,t79]) ).
cnf(t3831,plain,
true = p2(f4(X1,c21),f4(X1,c19)),
inference(step,[status(thm)],[t2640,t34]) ).
cnf(t2641,plain,
p2(f4(X1,c21),f4(X1,c19)) = true,
inference(orient,[status(thm)],[t3831]) ).
cnf(t2642,plain,
true = ifeq(true,true,p2(f4(X1,c19),f4(X1,c21)),true),
inference(cp,[status(thm)],[t481,t2641]) ).
cnf(t3832,plain,
true = p2(f4(X1,c19),f4(X1,c21)),
inference(step,[status(thm)],[t2642,t34]) ).
cnf(t2655,plain,
p2(f4(X1,c19),f4(X1,c21)) = true,
inference(orient,[status(thm)],[t3832]) ).
cnf(t3934,plain,
true = ifeq(true,true,ifeq(p2(c20,c20),true,false,true),true),
inference(step,[status(thm)],[t3547,t2655]) ).
cnf(t3935,plain,
true = ifeq(p2(c20,c20),true,false,true),
inference(step,[status(thm)],[t3934,t34]) ).
cnf(t3936,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t3935,t79]) ).
cnf(t3937,plain,
true = false,
inference(step,[status(thm)],[t3936,t34]) ).
cnf(t3549,plain,
false = true,
inference(orient,[status(thm)],[t3937]) ).
cnf(f5,negated_conjecture,
~ p12(f13(c20),f13(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_6) ).
fof(f5_nnf,plain,
~ p12(f13(c20),f13(c18)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ p12(f13(c20),f13(c18)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ p12(f13(c20),f13(c18)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f22,negated_conjecture,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_23) ).
fof(f22_nnf,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c18,c22]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3549]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN587-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 01:49:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.47/3.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.47/3.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------