%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP679-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 01:28:01 PM UTC 2026
% Result : Unsatisfiable 5.72s 21.48s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 9
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 4 RR)
% Number of literals : 87 ( 86 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t7,axiom,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(orient,[status(thm)],[t7]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t26,plain,
mult(X1,mult(unit,mult(X1,X2))) = mult(mult(X1,X1),X2),
inference(cp,[status(thm)],[t22,t10]) ).
cnf(t2840,plain,
mult(X1,mult(X1,X2)) = mult(mult(X1,X1),X2),
inference(step,[status(thm)],[t26,t10]) ).
cnf(t64,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t2840]) ).
cnf(t5,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t25,plain,
mult(X1,mult(rd(X2,X1),mult(X1,X3))) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t22,t12]) ).
cnf(t565,plain,
mult(X1,mult(rd(X2,X1),mult(X1,X3))) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t25]) ).
cnf(t3,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t596,plain,
mult(mult(X1,X2),ld(X1,X3)) = mult(X1,mult(rd(X2,X1),X3)),
inference(cp,[status(thm)],[t565,t8]) ).
cnf(t629,plain,
mult(mult(X1,X2),ld(X1,X3)) = mult(X1,mult(rd(X2,X1),X3)),
inference(orient,[status(thm)],[t596]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t634,plain,
mult(X1,mult(rd(unit,X1),X2)) = mult(X1,ld(X1,X2)),
inference(cp,[status(thm)],[t629,t9]) ).
cnf(t2847,plain,
mult(X1,mult(rd(unit,X1),X2)) = X2,
inference(step,[status(thm)],[t634,t8]) ).
cnf(t661,plain,
mult(X1,mult(rd(unit,X1),X2)) = X2,
inference(orient,[status(thm)],[t2847]) ).
cnf(t671,plain,
unit = mult(X1,rd(unit,X1)),
inference(cp,[status(thm)],[t661,t9]) ).
cnf(t701,plain,
mult(X1,rd(unit,X1)) = unit,
inference(orient,[status(thm)],[t671]) ).
cnf(t716,plain,
mult(mult(X1,X2),rd(unit,X1)) = mult(X1,mult(rd(X2,X1),unit)),
inference(cp,[status(thm)],[t565,t701]) ).
cnf(t2860,plain,
mult(mult(X1,X2),rd(unit,X1)) = mult(X1,rd(X2,X1)),
inference(step,[status(thm)],[t716,t9]) ).
cnf(t1119,plain,
mult(mult(X1,X2),rd(unit,X1)) = mult(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t2860]) ).
cnf(t6,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t15,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t14,t8]) ).
cnf(t44,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t670,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t661,t8]) ).
cnf(t736,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t670]) ).
cnf(t748,plain,
rd(unit,X1) = rd(X2,mult(X1,X2)),
inference(cp,[status(thm)],[t44,t736]) ).
cnf(t825,plain,
rd(X1,mult(X2,X1)) = rd(unit,X2),
inference(orient,[status(thm)],[t748]) ).
cnf(t836,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(cp,[status(thm)],[t825,t12]) ).
cnf(t897,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t836]) ).
cnf(t71,plain,
mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2),
inference(cp,[status(thm)],[t14,t64]) ).
cnf(t74,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(orient,[status(thm)],[t71]) ).
cnf(t4,axiom,
mult(op_c,X1) = mult(X1,op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t31,plain,
mult(X1,op_c) = mult(op_c,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t83,plain,
mult(op_c,op_c) = rd(mult(op_c,mult(X1,op_c)),X1),
inference(cp,[status(thm)],[t74,t31]) ).
cnf(t127,plain,
rd(mult(op_c,mult(X1,op_c)),X1) = mult(op_c,op_c),
inference(orient,[status(thm)],[t83]) ).
cnf(t903,plain,
rd(X1,mult(op_c,mult(X1,op_c))) = rd(unit,mult(op_c,op_c)),
inference(cp,[status(thm)],[t897,t127]) ).
cnf(t1434,plain,
rd(X1,mult(op_c,mult(X1,op_c))) = rd(unit,mult(op_c,op_c)),
inference(orient,[status(thm)],[t903]) ).
cnf(t1441,plain,
mult(mult(op_c,mult(unit,op_c)),rd(X1,mult(op_c,mult(unit,op_c)))) = mult(mult(mult(op_c,mult(unit,op_c)),X1),rd(unit,mult(op_c,op_c))),
inference(cp,[status(thm)],[t1119,t1434]) ).
cnf(t2907,plain,
mult(op_c,mult(unit,mult(op_c,rd(X1,mult(op_c,mult(unit,op_c)))))) = mult(mult(mult(op_c,mult(unit,op_c)),X1),rd(unit,mult(op_c,op_c))),
inference(step,[status(thm)],[t1441,t22]) ).
cnf(t2908,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,mult(unit,op_c))))) = mult(mult(mult(op_c,mult(unit,op_c)),X1),rd(unit,mult(op_c,op_c))),
inference(step,[status(thm)],[t2907,t10]) ).
cnf(t2909,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(mult(mult(op_c,mult(unit,op_c)),X1),rd(unit,mult(op_c,op_c))),
inference(step,[status(thm)],[t2908,t10]) ).
cnf(t2910,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(mult(op_c,mult(unit,mult(op_c,X1))),rd(unit,mult(op_c,op_c))),
inference(step,[status(thm)],[t2909,t22]) ).
cnf(t2911,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(mult(op_c,mult(op_c,X1)),rd(unit,mult(op_c,op_c))),
inference(step,[status(thm)],[t2910,t10]) ).
cnf(t36,plain,
mult(op_c,mult(X1,mult(op_c,X2))) = mult(mult(op_c,mult(op_c,X1)),X2),
inference(cp,[status(thm)],[t22,t31]) ).
cnf(t230,plain,
mult(mult(op_c,mult(op_c,X1)),X2) = mult(op_c,mult(X1,mult(op_c,X2))),
inference(orient,[status(thm)],[t36]) ).
cnf(t2912,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(op_c,mult(X1,mult(op_c,rd(unit,mult(op_c,op_c))))),
inference(step,[status(thm)],[t2911,t230]) ).
cnf(t2,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t686,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(cp,[status(thm)],[t18,t661]) ).
cnf(t771,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t686]) ).
cnf(t775,plain,
ld(X1,op_c) = mult(op_c,rd(unit,X1)),
inference(cp,[status(thm)],[t771,t31]) ).
cnf(t849,plain,
mult(op_c,rd(unit,X1)) = ld(X1,op_c),
inference(orient,[status(thm)],[t775]) ).
cnf(t2913,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(op_c,mult(X1,ld(mult(op_c,op_c),op_c))),
inference(step,[status(thm)],[t2912,t849]) ).
cnf(t33,plain,
mult(op_c,rd(X1,op_c)) = X1,
inference(cp,[status(thm)],[t31,t12]) ).
cnf(t46,plain,
mult(op_c,rd(X1,op_c)) = X1,
inference(orient,[status(thm)],[t33]) ).
cnf(t1129,plain,
mult(op_c,rd(rd(X1,op_c),op_c)) = mult(X1,rd(unit,op_c)),
inference(cp,[status(thm)],[t1119,t46]) ).
cnf(t2861,plain,
rd(X1,op_c) = mult(X1,rd(unit,op_c)),
inference(step,[status(thm)],[t1129,t46]) ).
cnf(t1155,plain,
mult(X1,rd(unit,op_c)) = rd(X1,op_c),
inference(orient,[status(thm)],[t2861]) ).
cnf(t1164,plain,
rd(unit,op_c) = ld(X1,rd(X1,op_c)),
inference(cp,[status(thm)],[t18,t1155]) ).
cnf(t1171,plain,
ld(X1,rd(X1,op_c)) = rd(unit,op_c),
inference(orient,[status(thm)],[t1164]) ).
cnf(t35,plain,
X1 = rd(mult(op_c,X1),op_c),
inference(cp,[status(thm)],[t14,t31]) ).
cnf(t57,plain,
rd(mult(op_c,X1),op_c) = X1,
inference(orient,[status(thm)],[t35]) ).
cnf(t1180,plain,
rd(unit,op_c) = ld(mult(op_c,X1),X1),
inference(cp,[status(thm)],[t1171,t57]) ).
cnf(t1203,plain,
ld(mult(op_c,X1),X1) = rd(unit,op_c),
inference(orient,[status(thm)],[t1180]) ).
cnf(t2914,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(op_c,mult(X1,rd(unit,op_c))),
inference(step,[status(thm)],[t2913,t1203]) ).
cnf(t2915,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = mult(op_c,rd(X1,op_c)),
inference(step,[status(thm)],[t2914,t1155]) ).
cnf(t2916,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = X1,
inference(step,[status(thm)],[t2915,t46]) ).
cnf(t2427,plain,
mult(op_c,mult(op_c,rd(X1,mult(op_c,op_c)))) = X1,
inference(orient,[status(thm)],[t2916]) ).
cnf(t2442,plain,
mult(op_c,rd(mult(op_c,rd(X1,mult(op_c,op_c))),op_c)) = mult(X1,rd(unit,op_c)),
inference(cp,[status(thm)],[t1119,t2427]) ).
cnf(t2930,plain,
mult(op_c,rd(X1,mult(op_c,op_c))) = mult(X1,rd(unit,op_c)),
inference(step,[status(thm)],[t2442,t46]) ).
cnf(t2931,plain,
mult(op_c,rd(X1,mult(op_c,op_c))) = rd(X1,op_c),
inference(step,[status(thm)],[t2930,t1155]) ).
cnf(t2535,plain,
mult(op_c,rd(X1,mult(op_c,op_c))) = rd(X1,op_c),
inference(orient,[status(thm)],[t2931]) ).
cnf(t2541,plain,
rd(mult(X1,mult(op_c,op_c)),op_c) = mult(op_c,X1),
inference(cp,[status(thm)],[t2535,t14]) ).
cnf(t2751,plain,
rd(mult(X1,mult(op_c,op_c)),op_c) = mult(op_c,X1),
inference(orient,[status(thm)],[t2541]) ).
cnf(t2775,plain,
mult(X1,mult(op_c,op_c)) = mult(mult(op_c,X1),op_c),
inference(cp,[status(thm)],[t12,t2751]) ).
cnf(t2941,plain,
mult(X1,mult(op_c,op_c)) = mult(op_c,mult(op_c,X1)),
inference(step,[status(thm)],[t2775,t31]) ).
cnf(t2783,plain,
mult(X1,mult(op_c,op_c)) = mult(op_c,mult(op_c,X1)),
inference(orient,[status(thm)],[t2941]) ).
cnf(goal_0,negated_conjecture,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(op_c,mult(op_c,a)) != mult(a,mult(op_c,op_c)),
inference(rw,[status(thm)],[goal_0,t64]) ).
cnf(g0_1,plain,
mult(op_c,mult(op_c,a)) != mult(op_c,mult(op_c,a)),
inference(rw,[status(thm)],[g0_0,t2783]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP679-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/20.39 % Computer : n017.cluster.edu
% 0.10/20.39 % Model : x86_64 x86_64
% 0.10/20.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.39 % Memory : 8046.5625MB
% 0.10/20.39 % OS : Linux 6.8.0-71-generic
% 0.10/20.39 % CPULimit : 300
% 0.10/20.39 % WCLimit : 300
% 0.10/20.39 % DateTime : Wed Sep 23 15:36:20 UTC 2026
% 0.10/20.39 % CPUTime :
% 0.10/20.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.72/21.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.72/21.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------