%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:24:55 PM UTC 2026
% Result : Unsatisfiable 6.05s 1.24s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 38 RR)
% Number of literals : 56 ( 55 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
sFlat0 = inverse(b),
introduced(definition) ).
cnf(t31,plain,
inverse(b) = sFlat0,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat1 = inverse(a),
introduced(definition) ).
cnf(t27,plain,
inverse(a) = sFlat1,
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
sFlat2 = multiply(inverse(b),inverse(a)),
introduced(definition) ).
cnf(t20,plain,
multiply(inverse(b),inverse(a)) = sFlat2,
inference(orient,[status(thm)],[t7]) ).
cnf(t84,plain,
multiply(inverse(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t20,t27]) ).
cnf(t30,plain,
multiply(inverse(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t84]) ).
cnf(t85,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t30,t31]) ).
cnf(t47,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t85]) ).
cnf(t8,axiom,
sFlat3 = multiply(a,b),
introduced(definition) ).
cnf(t22,plain,
multiply(a,b) = sFlat3,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sFlat4 = inverse(multiply(a,b)),
introduced(definition) ).
cnf(t83,plain,
sFlat4 = inverse(sFlat3),
inference(step,[status(thm)],[t9,t22]) ).
cnf(t24,plain,
inverse(sFlat3) = sFlat4,
inference(orient,[status(thm)],[t83]) ).
cnf(t4,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t4]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t25,plain,
identity = multiply(sFlat4,sFlat3),
inference(cp,[status(thm)],[t17,t24]) ).
cnf(t35,plain,
multiply(sFlat4,sFlat3) = identity,
inference(orient,[status(thm)],[t25]) ).
cnf(t36,plain,
multiply(sFlat4,multiply(sFlat3,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t12,t35]) ).
cnf(t1,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t86,plain,
multiply(sFlat4,multiply(sFlat3,X1)) = X1,
inference(step,[status(thm)],[t36,t11]) ).
cnf(t49,plain,
multiply(sFlat4,multiply(sFlat3,X1)) = X1,
inference(orient,[status(thm)],[t86]) ).
cnf(t23,plain,
multiply(a,multiply(b,X1)) = multiply(sFlat3,X1),
inference(cp,[status(thm)],[t12,t22]) ).
cnf(t67,plain,
multiply(a,multiply(b,X1)) = multiply(sFlat3,X1),
inference(orient,[status(thm)],[t23]) ).
cnf(t2,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t33,plain,
identity = multiply(b,sFlat0),
inference(cp,[status(thm)],[t13,t31]) ).
cnf(t45,plain,
multiply(b,sFlat0) = identity,
inference(orient,[status(thm)],[t33]) ).
cnf(t46,plain,
multiply(b,multiply(sFlat0,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t12,t45]) ).
cnf(t93,plain,
multiply(b,multiply(sFlat0,X1)) = X1,
inference(step,[status(thm)],[t46,t11]) ).
cnf(t61,plain,
multiply(b,multiply(sFlat0,X1)) = X1,
inference(orient,[status(thm)],[t93]) ).
cnf(t62,plain,
sFlat1 = multiply(b,sFlat2),
inference(cp,[status(thm)],[t61,t47]) ).
cnf(t65,plain,
multiply(b,sFlat2) = sFlat1,
inference(orient,[status(thm)],[t62]) ).
cnf(t68,plain,
multiply(sFlat3,sFlat2) = multiply(a,sFlat1),
inference(cp,[status(thm)],[t67,t65]) ).
cnf(t29,plain,
identity = multiply(a,sFlat1),
inference(cp,[status(thm)],[t13,t27]) ).
cnf(t41,plain,
multiply(a,sFlat1) = identity,
inference(orient,[status(thm)],[t29]) ).
cnf(t95,plain,
multiply(sFlat3,sFlat2) = identity,
inference(step,[status(thm)],[t68,t41]) ).
cnf(t73,plain,
multiply(sFlat3,sFlat2) = identity,
inference(orient,[status(thm)],[t95]) ).
cnf(t75,plain,
sFlat2 = multiply(sFlat4,identity),
inference(cp,[status(thm)],[t49,t73]) ).
cnf(t0,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t96,plain,
sFlat2 = sFlat4,
inference(step,[status(thm)],[t75,t10]) ).
cnf(t76,plain,
sFlat4 = sFlat2,
inference(orient,[status(thm)],[t96]) ).
cnf(t97,plain,
inverse(sFlat3) = sFlat2,
inference(step,[status(thm)],[t24,t76]) ).
cnf(t77,plain,
inverse(sFlat3) = sFlat2,
inference(orient,[status(thm)],[t97]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(sFlat0,inverse(a)) != inverse(multiply(a,b)),
inference(rw,[status(thm)],[goal_0,t31]) ).
cnf(g0_1,plain,
multiply(sFlat0,sFlat1) != inverse(multiply(a,b)),
inference(rw,[status(thm)],[g0_0,t27]) ).
cnf(g0_2,plain,
sFlat2 != inverse(multiply(a,b)),
inference(rw,[status(thm)],[g0_1,t47]) ).
cnf(g0_3,plain,
sFlat2 != inverse(sFlat3),
inference(rw,[status(thm)],[g0_2,t22]) ).
cnf(g0_4,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_3,t77]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.36 % Computer : n004.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Sep 23 13:13:20 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.05/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.05/1.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------