%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN608-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 03:35:19 PM UTC 2026
% Result : Unsatisfiable 73.60s 10.46s
% Output : Proof 73.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 48 unt; 0 def)
% Number of atoms : 96 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 50 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 82 ( 3 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,negated_conjecture,
( ~ p3(X18,X20)
| ~ p3(X18,X19)
| p3(X19,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_19) ).
fof(f18_nnf,plain,
! [X19,X20,X18] :
( ~ p3(X18,X20)
| ~ p3(X18,X19)
| p3(X19,X20) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X19,X20,X18] :
( ~ p3(X18,X20)
| ~ p3(X18,X19)
| p3(X19,X20) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ p3(X2,X1)
| ~ p3(X2,X0)
| p3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p3(X0,X2),true,p3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f5,negated_conjecture,
p3(f12(c22,c21),f15(c22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_6) ).
fof(f5_nnf,plain,
p3(f12(c22,c21),f15(c22)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p3(f12(c22,c21),f15(c22)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi3,negated_conjecture,
p3(f12(c22,c21),f15(c22)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f3,negated_conjecture,
p3(X18,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_4) ).
fof(f3_nnf,plain,
! [X18] : p3(X18,X18),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X18] : p3(X18,X18),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h10,plain,
p3(f15(c22),f12(c22,c21)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi3,hi2]) ).
cnf(f23,negated_conjecture,
( ~ p3(X22,X24)
| ~ p3(X21,X23)
| p3(f10(X21,X22),f10(X23,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_24) ).
fof(f23_nnf,plain,
! [X21,X22,X23,X24] :
( ~ p3(X22,X24)
| ~ p3(X21,X23)
| p3(f10(X21,X22),f10(X23,X24)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X21,X22,X23,X24] :
( ~ p3(X22,X24)
| ~ p3(X21,X23)
| p3(f10(X21,X22),f10(X23,X24)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ p3(X1,X3)
| ~ p3(X0,X2)
| p3(f10(X0,X1),f10(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi20,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p3(X2,X3),true,p3(f10(X0,X2),f10(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h43,plain,
p3(f10(V0,f15(c22)),f10(V0,f12(c22,c21))) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi2,h10]) ).
cnf(f11,negated_conjecture,
( ~ p3(X16,X17)
| p2(f9(X16),f9(X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
! [X16,X17] :
( ~ p3(X16,X17)
| p2(f9(X16),f9(X17)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X16,X17] :
( ~ p3(X16,X17)
| p2(f9(X16),f9(X17)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p3(X0,X1)
| p2(f9(X0),f9(X1)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p3(X0,X1),true,p2(f9(X0),f9(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h1177,plain,
p2(f9(f10(V0,f15(c22))),f9(f10(V0,f12(c22,c21)))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h43]) ).
cnf(f19,negated_conjecture,
( ~ p17(X4,X5)
| ~ p2(X5,X3)
| ~ p2(X4,X2)
| p17(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_20) ).
fof(f19_nnf,plain,
! [X2,X3,X4,X5] :
( ~ p17(X4,X5)
| ~ p2(X5,X3)
| ~ p2(X4,X2)
| p17(X2,X3) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X2,X3,X4,X5] :
( ~ p17(X4,X5)
| ~ p2(X5,X3)
| ~ p2(X4,X2)
| p17(X2,X3) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p17(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p17(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,ifeq(p17(X0,X2),true,p17(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f1,negated_conjecture,
p2(X11,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_2) ).
fof(f1_nnf,plain,
! [X11] : p2(X11,X11),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X11] : p2(X11,X11),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f26,negated_conjecture,
p17(f9(f10(f14(f4(f9(c19)),c19),f15(c22))),f6(f7(f8(c20)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_27) ).
fof(f26_nnf,plain,
p17(f9(f10(f14(f4(f9(c19)),c19),f15(c22))),f6(f7(f8(c20)))),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
p17(f9(f10(f14(f4(f9(c19)),c19),f15(c22))),f6(f7(f8(c20)))),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi23,negated_conjecture,
p17(f9(f10(f14(f4(f9(c19)),c19),f15(c22))),f6(f7(f8(c20)))) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h4823,plain,
p17(f9(f10(f14(f4(f9(c19)),c19),f12(c22,c21))),f6(f7(f8(c20)))) = true,
inference(hyper_resolution,[status(thm)],[hi16,h1177,hi0,hi23]) ).
cnf(f28,negated_conjecture,
~ p17(f9(f10(f14(f4(f9(c19)),c19),f12(X50,c21))),f6(f7(f8(c20)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p17_29) ).
fof(f28_nnf,plain,
! [X50] : ~ p17(f9(f10(f14(f4(f9(c19)),c19),f12(X50,c21))),f6(f7(f8(c20)))),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X50] : ~ p17(f9(f10(f14(f4(f9(c19)),c19),f12(X50,c21))),f6(f7(f8(c20)))),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ p17(f9(f10(f14(f4(f9(c19)),c19),f12(X0,c21))),f6(f7(f8(c20)))),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi29,negated_conjecture,
ifeq(p17(f9(f10(f14(f4(f9(c19)),c19),f12(X0,c21))),f6(f7(f8(c20)))),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi29,h4823]) ).
cnf(t2380,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f0,negated_conjecture,
~ p16(c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21_is_not_p16_1) ).
fof(f0_nnf,plain,
~ p16(c21),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ p16(c21),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ p16(c21),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f4,negated_conjecture,
~ p5(c21,f7(c20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p5_5) ).
fof(f4_nnf,plain,
~ p5(c21,f7(c20)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ p5(c21,f7(c20)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ p5(c21,f7(c20)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f7,negated_conjecture,
~ p3(c19,f4(f6(f7(c20)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_8) ).
fof(f7_nnf,plain,
~ p3(c19,f4(f6(f7(c20)))),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ p3(c19,f4(f6(f7(c20)))),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ p3(c19,f4(f6(f7(c20)))),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c7,c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2380]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN608-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 01:55:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 73.60/10.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 73.60/10.46 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------