%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN088-1.010 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:33:47 PM UTC 2026
% Result : Unsatisfiable 6.53s 6.34s
% Output : Proof 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 23
% Syntax : Number of formulae : 162 ( 158 unt; 0 def)
% Number of atoms : 202 ( 123 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 96 ( 56 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 1 avg)
% Maximal term depth : 21 ( 3 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-10 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-4 aty)
% Number of variables : 246 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t22,axiom,
sFlat0 = ap2(p,a),
introduced(definition) ).
cnf(t50,plain,
ap2(p,a) = sFlat0,
inference(orient,[status(thm)],[t22]) ).
cnf(t23,axiom,
sFlat1 = ap2(ap2(p,a),a),
introduced(definition) ).
cnf(t48,plain,
ap2(ap2(p,a),a) = sFlat1,
inference(orient,[status(thm)],[t23]) ).
cnf(t270,plain,
ap2(sFlat0,a) = sFlat1,
inference(step,[status(thm)],[t48,t50]) ).
cnf(t51,plain,
ap2(sFlat0,a) = sFlat1,
inference(rw,[status(thm)],[t270]) ).
cnf(t102,plain,
ap2(sFlat0,a) = sFlat1,
inference(orient,[status(thm)],[t51]) ).
cnf(t24,axiom,
sFlat2 = ap2(ap2(ap2(p,a),a),a),
introduced(definition) ).
cnf(t46,plain,
ap2(ap2(ap2(p,a),a),a) = sFlat2,
inference(orient,[status(thm)],[t24]) ).
cnf(t269,plain,
ap2(sFlat1,a) = sFlat2,
inference(step,[status(thm)],[t46,t48]) ).
cnf(t49,plain,
ap2(sFlat1,a) = sFlat2,
inference(rw,[status(thm)],[t269]) ).
cnf(t101,plain,
ap2(sFlat1,a) = sFlat2,
inference(orient,[status(thm)],[t49]) ).
cnf(t25,axiom,
sFlat3 = ap2(ap2(ap2(ap2(p,a),a),a),a),
introduced(definition) ).
cnf(t44,plain,
ap2(ap2(ap2(ap2(p,a),a),a),a) = sFlat3,
inference(orient,[status(thm)],[t25]) ).
cnf(t268,plain,
ap2(sFlat2,a) = sFlat3,
inference(step,[status(thm)],[t44,t46]) ).
cnf(t47,plain,
ap2(sFlat2,a) = sFlat3,
inference(rw,[status(thm)],[t268]) ).
cnf(t100,plain,
ap2(sFlat2,a) = sFlat3,
inference(orient,[status(thm)],[t47]) ).
cnf(t26,axiom,
sFlat4 = ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),
introduced(definition) ).
cnf(t42,plain,
ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a) = sFlat4,
inference(orient,[status(thm)],[t26]) ).
cnf(t267,plain,
ap2(sFlat3,a) = sFlat4,
inference(step,[status(thm)],[t42,t44]) ).
cnf(t45,plain,
ap2(sFlat3,a) = sFlat4,
inference(rw,[status(thm)],[t267]) ).
cnf(t99,plain,
ap2(sFlat3,a) = sFlat4,
inference(orient,[status(thm)],[t45]) ).
cnf(t27,axiom,
sFlat5 = ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),
introduced(definition) ).
cnf(t40,plain,
ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a) = sFlat5,
inference(orient,[status(thm)],[t27]) ).
cnf(t266,plain,
ap2(sFlat4,a) = sFlat5,
inference(step,[status(thm)],[t40,t42]) ).
cnf(t43,plain,
ap2(sFlat4,a) = sFlat5,
inference(rw,[status(thm)],[t266]) ).
cnf(t98,plain,
ap2(sFlat4,a) = sFlat5,
inference(orient,[status(thm)],[t43]) ).
cnf(t28,axiom,
sFlat6 = ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),
introduced(definition) ).
cnf(t38,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a) = sFlat6,
inference(orient,[status(thm)],[t28]) ).
cnf(t265,plain,
ap2(sFlat5,a) = sFlat6,
inference(step,[status(thm)],[t38,t40]) ).
cnf(t41,plain,
ap2(sFlat5,a) = sFlat6,
inference(rw,[status(thm)],[t265]) ).
cnf(t97,plain,
ap2(sFlat5,a) = sFlat6,
inference(orient,[status(thm)],[t41]) ).
cnf(t29,axiom,
sFlat7 = ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),
introduced(definition) ).
cnf(t36,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a) = sFlat7,
inference(orient,[status(thm)],[t29]) ).
cnf(t264,plain,
ap2(sFlat6,a) = sFlat7,
inference(step,[status(thm)],[t36,t38]) ).
cnf(t39,plain,
ap2(sFlat6,a) = sFlat7,
inference(rw,[status(thm)],[t264]) ).
cnf(t96,plain,
ap2(sFlat6,a) = sFlat7,
inference(orient,[status(thm)],[t39]) ).
cnf(t30,axiom,
sFlat8 = ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),a),
introduced(definition) ).
cnf(t34,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),a) = sFlat8,
inference(orient,[status(thm)],[t30]) ).
cnf(t263,plain,
ap2(sFlat7,a) = sFlat8,
inference(step,[status(thm)],[t34,t36]) ).
cnf(t37,plain,
ap2(sFlat7,a) = sFlat8,
inference(rw,[status(thm)],[t263]) ).
cnf(t95,plain,
ap2(sFlat7,a) = sFlat8,
inference(orient,[status(thm)],[t37]) ).
cnf(t31,axiom,
sFlat9 = ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),a),a),
introduced(definition) ).
cnf(t33,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),a),a) = sFlat9,
inference(orient,[status(thm)],[t31]) ).
cnf(t262,plain,
ap2(sFlat8,a) = sFlat9,
inference(step,[status(thm)],[t33,t34]) ).
cnf(t35,plain,
ap2(sFlat8,a) = sFlat9,
inference(rw,[status(thm)],[t262]) ).
cnf(t94,plain,
ap2(sFlat8,a) = sFlat9,
inference(orient,[status(thm)],[t35]) ).
cnf(f1,axiom,
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_1) ).
fof(f1_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ q_10(X9)
| ~ q_9(X8)
| ~ q_8(X7)
| ~ q_7(X6)
| ~ q_6(X5)
| ~ q_5(X4)
| ~ q_4(X3)
| ~ q_3(X2)
| ~ q_2(X1)
| ~ q_1(X0)
| p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t21,plain,
ifeq(q_1(X1),true,ifeq(q_2(X2),true,ifeq(q_3(X3),true,ifeq(q_4(X4),true,ifeq(q_5(X5),true,ifeq(q_6(X6),true,ifeq(q_7(X7),true,ifeq(q_8(X8),true,ifeq(q_9(X9),true,ifeq(q_10(X10),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,X1),X2),X3),X4),X5),X6),X7),X8),X9),X10),true),true),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t52,plain,
ifeq(q_1(X1),true,ifeq(q_2(X2),true,ifeq(q_3(X3),true,ifeq(q_4(X4),true,ifeq(q_5(X5),true,ifeq(q_6(X6),true,ifeq(q_7(X7),true,ifeq(q_8(X8),true,ifeq(q_9(X9),true,ifeq(q_10(X10),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,X1),X2),X3),X4),X5),X6),X7),X8),X9),X10),true),true),true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t53,plain,
true = ifeq(q_1(a),true,ifeq(q_2(X1),true,ifeq(q_3(X2),true,ifeq(q_4(X3),true,ifeq(q_5(X4),true,ifeq(q_6(X5),true,ifeq(q_7(X6),true,ifeq(q_8(X7),true,ifeq(q_9(X8),true,ifeq(q_10(X9),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat0,X1),X2),X3),X4),X5),X6),X7),X8),X9),true),true),true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t52,t50]) ).
cnf(f2,axiom,
q_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_2) ).
fof(f2_nnf,plain,
q_1(a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
q_1(a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t0,plain,
q_1(a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t54,plain,
q_1(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t271,plain,
true = ifeq(true,true,ifeq(q_2(X1),true,ifeq(q_3(X2),true,ifeq(q_4(X3),true,ifeq(q_5(X4),true,ifeq(q_6(X5),true,ifeq(q_7(X6),true,ifeq(q_8(X7),true,ifeq(q_9(X8),true,ifeq(q_10(X9),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat0,X1),X2),X3),X4),X5),X6),X7),X8),X9),true),true),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t53,t54]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t272,plain,
true = ifeq(q_2(X1),true,ifeq(q_3(X2),true,ifeq(q_4(X3),true,ifeq(q_5(X4),true,ifeq(q_6(X5),true,ifeq(q_7(X6),true,ifeq(q_8(X7),true,ifeq(q_9(X8),true,ifeq(q_10(X9),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat0,X1),X2),X3),X4),X5),X6),X7),X8),X9),true),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t271,t32]) ).
cnf(t103,plain,
ifeq(q_2(X1),true,ifeq(q_3(X2),true,ifeq(q_4(X3),true,ifeq(q_5(X4),true,ifeq(q_6(X5),true,ifeq(q_7(X6),true,ifeq(q_8(X7),true,ifeq(q_9(X8),true,ifeq(q_10(X9),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat0,X1),X2),X3),X4),X5),X6),X7),X8),X9),true),true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t272]) ).
cnf(t122,plain,
true = ifeq(q_2(a),true,ifeq(q_3(X1),true,ifeq(q_4(X2),true,ifeq(q_5(X3),true,ifeq(q_6(X4),true,ifeq(q_7(X5),true,ifeq(q_8(X6),true,ifeq(q_9(X7),true,ifeq(q_10(X8),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat1,X1),X2),X3),X4),X5),X6),X7),X8),true),true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t103,t102]) ).
cnf(f4,axiom,
q_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_4) ).
fof(f4_nnf,plain,
q_2(a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
q_2(a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t4,plain,
q_2(a) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t58,plain,
q_2(a) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t273,plain,
true = ifeq(true,true,ifeq(q_3(X1),true,ifeq(q_4(X2),true,ifeq(q_5(X3),true,ifeq(q_6(X4),true,ifeq(q_7(X5),true,ifeq(q_8(X6),true,ifeq(q_9(X7),true,ifeq(q_10(X8),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat1,X1),X2),X3),X4),X5),X6),X7),X8),true),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t122,t58]) ).
cnf(t274,plain,
true = ifeq(q_3(X1),true,ifeq(q_4(X2),true,ifeq(q_5(X3),true,ifeq(q_6(X4),true,ifeq(q_7(X5),true,ifeq(q_8(X6),true,ifeq(q_9(X7),true,ifeq(q_10(X8),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat1,X1),X2),X3),X4),X5),X6),X7),X8),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t273,t32]) ).
cnf(t123,plain,
ifeq(q_3(X1),true,ifeq(q_4(X2),true,ifeq(q_5(X3),true,ifeq(q_6(X4),true,ifeq(q_7(X5),true,ifeq(q_8(X6),true,ifeq(q_9(X7),true,ifeq(q_10(X8),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat1,X1),X2),X3),X4),X5),X6),X7),X8),true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t274]) ).
cnf(t140,plain,
true = ifeq(q_3(a),true,ifeq(q_4(X1),true,ifeq(q_5(X2),true,ifeq(q_6(X3),true,ifeq(q_7(X4),true,ifeq(q_8(X5),true,ifeq(q_9(X6),true,ifeq(q_10(X7),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat2,X1),X2),X3),X4),X5),X6),X7),true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t123,t101]) ).
cnf(f6,axiom,
q_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_6) ).
fof(f6_nnf,plain,
q_3(a),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
q_3(a),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t6,plain,
q_3(a) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t62,plain,
q_3(a) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t275,plain,
true = ifeq(true,true,ifeq(q_4(X1),true,ifeq(q_5(X2),true,ifeq(q_6(X3),true,ifeq(q_7(X4),true,ifeq(q_8(X5),true,ifeq(q_9(X6),true,ifeq(q_10(X7),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat2,X1),X2),X3),X4),X5),X6),X7),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t140,t62]) ).
cnf(t276,plain,
true = ifeq(q_4(X1),true,ifeq(q_5(X2),true,ifeq(q_6(X3),true,ifeq(q_7(X4),true,ifeq(q_8(X5),true,ifeq(q_9(X6),true,ifeq(q_10(X7),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat2,X1),X2),X3),X4),X5),X6),X7),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t275,t32]) ).
cnf(t141,plain,
ifeq(q_4(X1),true,ifeq(q_5(X2),true,ifeq(q_6(X3),true,ifeq(q_7(X4),true,ifeq(q_8(X5),true,ifeq(q_9(X6),true,ifeq(q_10(X7),true,ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat2,X1),X2),X3),X4),X5),X6),X7),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t276]) ).
cnf(t156,plain,
true = ifeq(q_4(a),true,ifeq(q_5(X1),true,ifeq(q_6(X2),true,ifeq(q_7(X3),true,ifeq(q_8(X4),true,ifeq(q_9(X5),true,ifeq(q_10(X6),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,X1),X2),X3),X4),X5),X6),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t141,t100]) ).
cnf(f8,axiom,
q_4(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_8) ).
fof(f8_nnf,plain,
q_4(a),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
q_4(a),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t8,plain,
q_4(a) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t66,plain,
q_4(a) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t277,plain,
true = ifeq(true,true,ifeq(q_5(X1),true,ifeq(q_6(X2),true,ifeq(q_7(X3),true,ifeq(q_8(X4),true,ifeq(q_9(X5),true,ifeq(q_10(X6),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,X1),X2),X3),X4),X5),X6),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t156,t66]) ).
cnf(t278,plain,
true = ifeq(q_5(X1),true,ifeq(q_6(X2),true,ifeq(q_7(X3),true,ifeq(q_8(X4),true,ifeq(q_9(X5),true,ifeq(q_10(X6),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,X1),X2),X3),X4),X5),X6),true),true),true),true),true),true),
inference(step,[status(thm)],[t277,t32]) ).
cnf(t157,plain,
ifeq(q_5(X1),true,ifeq(q_6(X2),true,ifeq(q_7(X3),true,ifeq(q_8(X4),true,ifeq(q_9(X5),true,ifeq(q_10(X6),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,X1),X2),X3),X4),X5),X6),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t278]) ).
cnf(f10,axiom,
q_5(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_10) ).
fof(f10_nnf,plain,
q_5(a),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
q_5(a),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t10,plain,
q_5(a) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t70,plain,
q_5(a) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t158,plain,
true = ifeq(true,true,ifeq(q_6(X1),true,ifeq(q_7(X2),true,ifeq(q_8(X3),true,ifeq(q_9(X4),true,ifeq(q_10(X5),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,a),X1),X2),X3),X4),X5),true),true),true),true),true),true),
inference(cp,[status(thm)],[t157,t70]) ).
cnf(t279,plain,
true = ifeq(q_6(X1),true,ifeq(q_7(X2),true,ifeq(q_8(X3),true,ifeq(q_9(X4),true,ifeq(q_10(X5),true,ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,a),X1),X2),X3),X4),X5),true),true),true),true),true),
inference(step,[status(thm)],[t158,t32]) ).
cnf(t280,plain,
true = ifeq(q_6(X1),true,ifeq(q_7(X2),true,ifeq(q_8(X3),true,ifeq(q_9(X4),true,ifeq(q_10(X5),true,ap2(ap2(ap2(ap2(ap2(sFlat4,X1),X2),X3),X4),X5),true),true),true),true),true),
inference(step,[status(thm)],[t279,t99]) ).
cnf(t171,plain,
ifeq(q_6(X1),true,ifeq(q_7(X2),true,ifeq(q_8(X3),true,ifeq(q_9(X4),true,ifeq(q_10(X5),true,ap2(ap2(ap2(ap2(ap2(sFlat4,X1),X2),X3),X4),X5),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t280]) ).
cnf(f12,axiom,
q_6(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_12) ).
fof(f12_nnf,plain,
q_6(a),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
q_6(a),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t12,plain,
q_6(a) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t78,plain,
q_6(a) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t172,plain,
true = ifeq(true,true,ifeq(q_7(X1),true,ifeq(q_8(X2),true,ifeq(q_9(X3),true,ifeq(q_10(X4),true,ap2(ap2(ap2(ap2(ap2(sFlat4,a),X1),X2),X3),X4),true),true),true),true),true),
inference(cp,[status(thm)],[t171,t78]) ).
cnf(t281,plain,
true = ifeq(q_7(X1),true,ifeq(q_8(X2),true,ifeq(q_9(X3),true,ifeq(q_10(X4),true,ap2(ap2(ap2(ap2(ap2(sFlat4,a),X1),X2),X3),X4),true),true),true),true),
inference(step,[status(thm)],[t172,t32]) ).
cnf(t282,plain,
true = ifeq(q_7(X1),true,ifeq(q_8(X2),true,ifeq(q_9(X3),true,ifeq(q_10(X4),true,ap2(ap2(ap2(ap2(sFlat5,X1),X2),X3),X4),true),true),true),true),
inference(step,[status(thm)],[t281,t98]) ).
cnf(t183,plain,
ifeq(q_7(X1),true,ifeq(q_8(X2),true,ifeq(q_9(X3),true,ifeq(q_10(X4),true,ap2(ap2(ap2(ap2(sFlat5,X1),X2),X3),X4),true),true),true),true) = true,
inference(orient,[status(thm)],[t282]) ).
cnf(f14,axiom,
q_7(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_14) ).
fof(f14_nnf,plain,
q_7(a),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
q_7(a),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t14,plain,
q_7(a) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t74,plain,
q_7(a) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t184,plain,
true = ifeq(true,true,ifeq(q_8(X1),true,ifeq(q_9(X2),true,ifeq(q_10(X3),true,ap2(ap2(ap2(ap2(sFlat5,a),X1),X2),X3),true),true),true),true),
inference(cp,[status(thm)],[t183,t74]) ).
cnf(t283,plain,
true = ifeq(q_8(X1),true,ifeq(q_9(X2),true,ifeq(q_10(X3),true,ap2(ap2(ap2(ap2(sFlat5,a),X1),X2),X3),true),true),true),
inference(step,[status(thm)],[t184,t32]) ).
cnf(t284,plain,
true = ifeq(q_8(X1),true,ifeq(q_9(X2),true,ifeq(q_10(X3),true,ap2(ap2(ap2(sFlat6,X1),X2),X3),true),true),true),
inference(step,[status(thm)],[t283,t97]) ).
cnf(t193,plain,
ifeq(q_8(X1),true,ifeq(q_9(X2),true,ifeq(q_10(X3),true,ap2(ap2(ap2(sFlat6,X1),X2),X3),true),true),true) = true,
inference(orient,[status(thm)],[t284]) ).
cnf(f16,axiom,
q_8(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_16) ).
fof(f16_nnf,plain,
q_8(a),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
q_8(a),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t16,plain,
q_8(a) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t90,plain,
q_8(a) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t194,plain,
true = ifeq(true,true,ifeq(q_9(X1),true,ifeq(q_10(X2),true,ap2(ap2(ap2(sFlat6,a),X1),X2),true),true),true),
inference(cp,[status(thm)],[t193,t90]) ).
cnf(t285,plain,
true = ifeq(q_9(X1),true,ifeq(q_10(X2),true,ap2(ap2(ap2(sFlat6,a),X1),X2),true),true),
inference(step,[status(thm)],[t194,t32]) ).
cnf(t286,plain,
true = ifeq(q_9(X1),true,ifeq(q_10(X2),true,ap2(ap2(sFlat7,X1),X2),true),true),
inference(step,[status(thm)],[t285,t96]) ).
cnf(t201,plain,
ifeq(q_9(X1),true,ifeq(q_10(X2),true,ap2(ap2(sFlat7,X1),X2),true),true) = true,
inference(orient,[status(thm)],[t286]) ).
cnf(f18,axiom,
q_9(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_18) ).
fof(f18_nnf,plain,
q_9(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
q_9(a),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t18,plain,
q_9(a) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t86,plain,
q_9(a) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t202,plain,
true = ifeq(true,true,ifeq(q_10(X1),true,ap2(ap2(sFlat7,a),X1),true),true),
inference(cp,[status(thm)],[t201,t86]) ).
cnf(t287,plain,
true = ifeq(q_10(X1),true,ap2(ap2(sFlat7,a),X1),true),
inference(step,[status(thm)],[t202,t32]) ).
cnf(t288,plain,
true = ifeq(q_10(X1),true,ap2(sFlat8,X1),true),
inference(step,[status(thm)],[t287,t95]) ).
cnf(t207,plain,
ifeq(q_10(X1),true,ap2(sFlat8,X1),true) = true,
inference(orient,[status(thm)],[t288]) ).
cnf(f20,axiom,
q_10(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_20) ).
fof(f20_nnf,plain,
q_10(a),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
q_10(a),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(t2,plain,
q_10(a) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t82,plain,
q_10(a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t208,plain,
true = ifeq(true,true,ap2(sFlat8,a),true),
inference(cp,[status(thm)],[t207,t82]) ).
cnf(t289,plain,
true = ap2(sFlat8,a),
inference(step,[status(thm)],[t208,t32]) ).
cnf(t290,plain,
true = sFlat9,
inference(step,[status(thm)],[t289,t94]) ).
cnf(t211,plain,
true = sFlat9,
inference(orient,[status(thm)],[t290]) ).
cnf(f0,negated_conjecture,
~ p(a,a,a,a,a,a,a,a,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_goal_1) ).
fof(f0_nnf,plain,
~ p(a,a,a,a,a,a,a,a,a,a),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ p(a,a,a,a,a,a,a,a,a,a),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ p(a,a,a,a,a,a,a,a,a,a),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(p,a),a),a),a),a),a),a),a),a),a) != true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat0,a),a),a),a),a),a),a),a),a) != true,
inference(rw,[status(thm)],[goal_0,t50]) ).
cnf(g0_1,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat1,a),a),a),a),a),a),a),a) != true,
inference(rw,[status(thm)],[g0_0,t102]) ).
cnf(g0_2,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(sFlat2,a),a),a),a),a),a),a) != true,
inference(rw,[status(thm)],[g0_1,t101]) ).
cnf(g0_3,plain,
ap2(ap2(ap2(ap2(ap2(ap2(sFlat3,a),a),a),a),a),a) != true,
inference(rw,[status(thm)],[g0_2,t100]) ).
cnf(g0_4,plain,
ap2(ap2(ap2(ap2(ap2(sFlat4,a),a),a),a),a) != true,
inference(rw,[status(thm)],[g0_3,t99]) ).
cnf(g0_5,plain,
ap2(ap2(ap2(ap2(sFlat5,a),a),a),a) != true,
inference(rw,[status(thm)],[g0_4,t98]) ).
cnf(g0_6,plain,
ap2(ap2(ap2(sFlat6,a),a),a) != true,
inference(rw,[status(thm)],[g0_5,t97]) ).
cnf(g0_7,plain,
ap2(ap2(sFlat7,a),a) != true,
inference(rw,[status(thm)],[g0_6,t96]) ).
cnf(g0_8,plain,
ap2(sFlat8,a) != true,
inference(rw,[status(thm)],[g0_7,t95]) ).
cnf(g0_9,plain,
sFlat9 != true,
inference(rw,[status(thm)],[g0_8,t94]) ).
cnf(g0_10,plain,
sFlat9 != sFlat9,
inference(rw,[status(thm)],[g0_9,t211]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN088-1.010 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 00:11:40 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.53/6.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.53/6.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------