%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN686-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 03:35:29 PM UTC 2026
% Result : Unsatisfiable 6.20s 1.28s
% Output : Proof 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 64 unt; 0 def)
% Number of atoms : 140 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 140 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f27,negated_conjecture,
( ~ p3(X57,X59)
| ~ p3(X57,X58)
| p3(X58,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_28) ).
fof(f27_nnf,plain,
! [X58,X59,X57] :
( ~ p3(X57,X59)
| ~ p3(X57,X58)
| p3(X58,X59) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X58,X59,X57] :
( ~ p3(X57,X59)
| ~ p3(X57,X58)
| p3(X58,X59) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( ~ p3(X2,X1)
| ~ p3(X2,X0)
| p3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi26,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p3(X0,X2),true,p3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(f16,negated_conjecture,
p3(c36,f7(c33,c34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_17) ).
fof(f16_nnf,plain,
p3(c36,f7(c33,c34)),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
p3(c36,f7(c33,c34)),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,negated_conjecture,
p3(c36,f7(c33,c34)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f5,negated_conjecture,
p3(X57,X57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_6) ).
fof(f5_nnf,plain,
! [X57] : p3(X57,X57),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X57] : p3(X57,X57),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h19,plain,
p3(f7(c33,c34),c36) = true,
inference(hyper_resolution,[status(thm)],[hi26,hi16,hi5]) ).
cnf(f49,negated_conjecture,
( ~ p3(X85,X87)
| ~ p2(X84,X86)
| p4(f5(X84,X85),f5(X86,X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_50) ).
fof(f49_nnf,plain,
! [X84,X85,X86,X87] :
( ~ p3(X85,X87)
| ~ p2(X84,X86)
| p4(f5(X84,X85),f5(X86,X87)) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X84,X85,X86,X87] :
( ~ p3(X85,X87)
| ~ p2(X84,X86)
| p4(f5(X84,X85),f5(X86,X87)) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p4(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(hi48,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p3(X2,X3),true,p4(f5(X0,X2),f5(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(f11,negated_conjecture,
p2(X27,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
! [X27] : p2(X27,X27),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X27] : p2(X27,X27),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h81,plain,
p4(f5(V0,f7(c33,c34)),f5(V0,c36)) = true,
inference(hyper_resolution,[status(thm)],[hi48,hi11,h19]) ).
cnf(f26,negated_conjecture,
( ~ p4(X81,X83)
| ~ p4(X81,X82)
| p4(X82,X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_27) ).
fof(f26_nnf,plain,
! [X82,X83,X81] :
( ~ p4(X81,X83)
| ~ p4(X81,X82)
| p4(X82,X83) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X82,X83,X81] :
( ~ p4(X81,X83)
| ~ p4(X81,X82)
| p4(X82,X83) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( ~ p4(X2,X1)
| ~ p4(X2,X0)
| p4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi25,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X0,X2),true,p4(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(f19,negated_conjecture,
p4(f5(c32,f7(c33,c34)),c35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_20) ).
fof(f19_nnf,plain,
p4(f5(c32,f7(c33,c34)),c35),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
p4(f5(c32,f7(c33,c34)),c35),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,negated_conjecture,
p4(f5(c32,f7(c33,c34)),c35) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h770,plain,
p4(f5(c32,c36),c35) = true,
inference(hyper_resolution,[status(thm)],[hi25,h81,hi19]) ).
cnf(f18,negated_conjecture,
p4(f5(c32,c36),c37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_19) ).
fof(f18_nnf,plain,
p4(f5(c32,c36),c37),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
p4(f5(c32,c36),c37),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,negated_conjecture,
p4(f5(c32,c36),c37) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h838,plain,
p4(c37,c35) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi18,h770]) ).
cnf(f40,negated_conjecture,
( ~ p8(X105,X107)
| ~ p4(X106,X108)
| p9(f10(X105,X106),f10(X107,X108)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_41) ).
fof(f40_nnf,plain,
! [X105,X106,X107,X108] :
( ~ p8(X105,X107)
| ~ p4(X106,X108)
| p9(f10(X105,X106),f10(X107,X108)) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [X105,X106,X107,X108] :
( ~ p8(X105,X107)
| ~ p4(X106,X108)
| p9(f10(X105,X106),f10(X107,X108)) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( ~ p8(X0,X2)
| ~ p4(X1,X3)
| p9(f10(X0,X1),f10(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi39,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p8(X2,X3),true,p9(f10(X2,X0),f10(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(f2,negated_conjecture,
p8(X91,X91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
fof(f2_nnf,plain,
! [X91] : p8(X91,X91),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X91] : p8(X91,X91),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p8(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p8(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h895,plain,
p9(f10(V0,c37),f10(V0,c35)) = true,
inference(hyper_resolution,[status(thm)],[hi39,h838,hi2]) ).
cnf(f38,negated_conjecture,
( ~ p30(X70,X71)
| ~ p9(X70,X68)
| ~ p4(X71,X69)
| p30(X68,X69) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30_39) ).
fof(f38_nnf,plain,
! [X68,X69,X71,X70] :
( ~ p30(X70,X71)
| ~ p9(X70,X68)
| ~ p4(X71,X69)
| p30(X68,X69) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [X68,X69,X71,X70] :
( ~ p30(X70,X71)
| ~ p9(X70,X68)
| ~ p4(X71,X69)
| p30(X68,X69) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( ~ p30(X3,X2)
| ~ p9(X3,X0)
| ~ p4(X2,X1)
| p30(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi37,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p9(X2,X3),true,ifeq(p30(X2,X0),true,p30(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(f4,negated_conjecture,
p4(X81,X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_5) ).
fof(f4_nnf,plain,
! [X81] : p4(X81,X81),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X81] : p4(X81,X81),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f20,negated_conjecture,
p30(f10(f12(c39,c36),c37),c41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30_21) ).
fof(f20_nnf,plain,
p30(f10(f12(c39,c36),c37),c41),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
p30(f10(f12(c39,c36),c37),c41),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,negated_conjecture,
p30(f10(f12(c39,c36),c37),c41) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h3004,plain,
p30(f10(f12(c39,c36),c35),c41) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi4,h895,hi20]) ).
cnf(f50,negated_conjecture,
( ~ p3(X95,X97)
| ~ p11(X94,X96)
| p8(f12(X94,X95),f12(X96,X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_51) ).
fof(f50_nnf,plain,
! [X94,X95,X96,X97] :
( ~ p3(X95,X97)
| ~ p11(X94,X96)
| p8(f12(X94,X95),f12(X96,X97)) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [X94,X95,X96,X97] :
( ~ p3(X95,X97)
| ~ p11(X94,X96)
| p8(f12(X94,X95),f12(X96,X97)) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c50,plain,
( ~ p3(X1,X3)
| ~ p11(X0,X2)
| p8(f12(X0,X1),f12(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(hi49,negated_conjecture,
ifeq(p11(X0,X1),true,ifeq(p3(X2,X3),true,p8(f12(X0,X2),f12(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(f0,negated_conjecture,
p11(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_1) ).
fof(f0_nnf,plain,
! [X0] : p11(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p11(X0,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p11(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p11(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h13,plain,
p8(f12(V0,c36),f12(V0,f7(c33,c34))) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi0,hi16]) ).
cnf(h119,plain,
p9(f10(f12(V0,c36),V1),f10(f12(V0,f7(c33,c34)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi4,h13]) ).
cnf(t38,plain,
p30(f10(f12(c39,f7(c33,c34)),c35),c41) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi4,h119,h3004]) ).
cnf(t536,plain,
p30(f10(f12(c39,f7(c33,c34)),c35),c41) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(f21,negated_conjecture,
~ p30(f10(f12(c39,f7(c33,c34)),c35),c41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p30_22) ).
fof(f21_nnf,plain,
~ p30(f10(f12(c39,f7(c33,c34)),c35),c41),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ p30(f10(f12(c39,f7(c33,c34)),c35),c41),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ p30(f10(f12(c39,f7(c33,c34)),c35),c41),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
p30(f10(f12(c39,f7(c33,c34)),c35),c41) != true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t536]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN686-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 02:05:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.20/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.20/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------