%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN585-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 12.87s 2.19s
% Output : Proof 12.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 62 unt; 0 def)
% Number of atoms : 94 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 34 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 92 ( 15 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,negated_conjecture,
~ p11(c18,f9(c12,f8(c16,c14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p11_12) ).
fof(f11_nnf,plain,
~ p11(c18,f9(c12,f8(c16,c14))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ p11(c18,f9(c12,f8(c16,c14))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ p11(c18,f9(c12,f8(c16,c14))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t15,plain,
p11(c18,f9(c12,f8(c16,c14))) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t233,plain,
p11(c18,f9(c12,f8(c16,c14))) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(f15,negated_conjecture,
( ~ p11(X14,X13)
| ~ p11(X12,X14)
| p11(X12,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_16) ).
fof(f15_nnf,plain,
! [X12,X13,X14] :
( ~ p11(X14,X13)
| ~ p11(X12,X14)
| p11(X12,X13) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X12,X13,X14] :
( ~ p11(X14,X13)
| ~ p11(X12,X14)
| p11(X12,X13) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ p11(X2,X1)
| ~ p11(X0,X2)
| p11(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t24,plain,
ifeq(p11(X1,X2),true,ifeq(p11(X2,X3),true,p11(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t129,plain,
ifeq(p11(X1,X2),true,ifeq(p11(X2,X3),true,p11(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(f6,negated_conjecture,
p11(c18,f9(c12,c14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_7) ).
fof(f6_nnf,plain,
p11(c18,f9(c12,c14)),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
p11(c18,f9(c12,c14)),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t11,plain,
p11(c18,f9(c12,c14)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t149,plain,
p11(c18,f9(c12,c14)) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t151,plain,
true = ifeq(true,true,ifeq(p11(f9(c12,c14),X1),true,p11(c18,X1),true),true),
inference(cp,[status(thm)],[t129,t149]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t13488,plain,
true = ifeq(p11(f9(c12,c14),X1),true,p11(c18,X1),true),
inference(step,[status(thm)],[t151,t35]) ).
cnf(t1093,plain,
ifeq(p11(f9(c12,c14),X1),true,p11(c18,X1),true) = true,
inference(orient,[status(thm)],[t13488]) ).
cnf(f25,negated_conjecture,
( ~ p11(X15,X16)
| p11(f9(X17,X15),f9(X17,X16))
| p2(X17,f3(c13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_26) ).
fof(f25_nnf,plain,
! [X17,X15,X16] :
( ~ p11(X15,X16)
| p11(f9(X17,X15),f9(X17,X16))
| p2(X17,f3(c13)) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X17,X15,X16] :
( ~ p11(X15,X16)
| p11(f9(X17,X15),f9(X17,X16))
| p2(X17,f3(c13)) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( ~ p11(X1,X2)
| p11(f9(X0,X1),f9(X0,X2))
| p2(X0,f3(c13)) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t26,plain,
ifeq(p11(X1,X2),true,or(p2(X3,f3(c13)),p11(f9(X3,X1),f9(X3,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t132,plain,
ifeq(p11(X1,X2),true,or(p2(X3,f3(c13)),p11(f9(X3,X1),f9(X3,X2))),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f5,negated_conjecture,
~ p2(c12,f3(c13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_6) ).
fof(f5_nnf,plain,
~ p2(c12,f3(c13)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ p2(c12,f3(c13)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ p2(c12,f3(c13)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t8,plain,
p2(c12,f3(c13)) = false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t189,plain,
p2(c12,f3(c13)) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t198,plain,
true = ifeq(p11(X1,X2),true,or(false,p11(f9(c12,X1),f9(c12,X2))),true),
inference(cp,[status(thm)],[t132,t189]) ).
cnf(t2,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t37,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t13823,plain,
true = ifeq(p11(X1,X2),true,p11(f9(c12,X1),f9(c12,X2)),true),
inference(step,[status(thm)],[t198,t37]) ).
cnf(t13010,plain,
ifeq(p11(X1,X2),true,p11(f9(c12,X1),f9(c12,X2)),true) = true,
inference(orient,[status(thm)],[t13823]) ).
cnf(f12,negated_conjecture,
( ~ p11(X9,X11)
| p11(X9,f8(X10,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_13) ).
fof(f12_nnf,plain,
! [X9,X10,X11] :
( ~ p11(X9,X11)
| p11(X9,f8(X10,X11)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X9,X10,X11] :
( ~ p11(X9,X11)
| p11(X9,f8(X10,X11)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ p11(X0,X2)
| p11(X0,f8(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t20,plain,
ifeq(p11(X1,X2),true,p11(X1,f8(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t130,plain,
ifeq(p11(X1,X2),true,p11(X1,f8(X3,X2)),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f1,negated_conjecture,
p11(X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_2) ).
fof(f1_nnf,plain,
! [X8] : p11(X8,X8),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X8] : p11(X8,X8),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p11(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t6,plain,
p11(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t137,plain,
p11(X1,X1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t138,plain,
true = ifeq(true,true,p11(X1,f8(X2,X1)),true),
inference(cp,[status(thm)],[t130,t137]) ).
cnf(t13438,plain,
true = p11(X1,f8(X2,X1)),
inference(step,[status(thm)],[t138,t35]) ).
cnf(t243,plain,
p11(X1,f8(X2,X1)) = true,
inference(orient,[status(thm)],[t13438]) ).
cnf(t13011,plain,
true = ifeq(true,true,p11(f9(c12,X1),f9(c12,f8(X2,X1))),true),
inference(cp,[status(thm)],[t13010,t243]) ).
cnf(t13824,plain,
true = p11(f9(c12,X1),f9(c12,f8(X2,X1))),
inference(step,[status(thm)],[t13011,t35]) ).
cnf(t13027,plain,
p11(f9(c12,X1),f9(c12,f8(X2,X1))) = true,
inference(orient,[status(thm)],[t13824]) ).
cnf(t13035,plain,
true = ifeq(true,true,p11(c18,f9(c12,f8(X1,c14))),true),
inference(cp,[status(thm)],[t1093,t13027]) ).
cnf(t13825,plain,
true = p11(c18,f9(c12,f8(X1,c14))),
inference(step,[status(thm)],[t13035,t35]) ).
cnf(t13044,plain,
p11(c18,f9(c12,f8(X1,c14))) = true,
inference(orient,[status(thm)],[t13825]) ).
cnf(t13826,plain,
true = false,
inference(step,[status(thm)],[t233,t13044]) ).
cnf(t13060,plain,
true = false,
inference(rw,[status(thm)],[t13826]) ).
cnf(t13393,plain,
false = true,
inference(orient,[status(thm)],[t13060]) ).
cnf(f4,negated_conjecture,
~ p2(c14,f3(c13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_5) ).
fof(f4_nnf,plain,
~ p2(c14,f3(c13)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ p2(c14,f3(c13)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ p2(c14,f3(c13)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f9,negated_conjecture,
~ p2(c12,f3(f4(c13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_10) ).
fof(f9_nnf,plain,
~ p2(c12,f3(f4(c13))),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ p2(c12,f3(f4(c13))),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ p2(c12,f3(f4(c13))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c5,c9,c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13393]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN585-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.33 % Computer : n018.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 25 01:49:49 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.87/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.87/2.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------