%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP054-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 01:30:23 PM UTC 2026
% Result : Unsatisfiable 50.00s 11.41s
% Output : CNFRefutation 50.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 2
% Syntax : Number of formulae : 92 ( 86 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 283 ( 0 sgn 283 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f3,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = X1,
inference(superposition,[status(thm)],[c_104,c_51]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1)) = X3,
inference(superposition,[status(thm)],[c_123,c_51]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)))) = X1,
inference(superposition,[status(thm)],[c_170,c_51]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2)))))))) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X1))),
inference(superposition,[status(thm)],[c_177,c_51]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)))) = X1,
inference(superposition,[status(thm)],[c_1265,c_51]) ).
tcf(c_2361,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(demodulation,[status(thm)],[c_1346,c_123]) ).
tcf(c_2394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,X2))),
inference(superposition,[status(thm)],[c_2361,c_51]) ).
tcf(c_2540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(X2,X3),inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X3))))))))),multiply(X0,multiply(X2,X3)))) = X1,
inference(superposition,[status(thm)],[c_2394,c_51]) ).
tcf(c_2622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(X2,multiply(X3,X4)),inverse(multiply(inverse(X5),X5)))))))),multiply(X0,multiply(X2,multiply(X3,X4))))) = X1,
inference(superposition,[status(thm)],[c_123,c_2540]) ).
tcf(c_4689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_123,c_2622]) ).
tcf(c_4702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(X4),X4)))))))),X1)) = X3,
inference(superposition,[status(thm)],[c_123,c_4689]) ).
tcf(c_4818,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(demodulation,[status(thm)],[c_1346,c_123]) ).
tcf(c_4855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),X1)) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X0,X2)))),
inference(superposition,[status(thm)],[c_4818,c_4702]) ).
tcf(c_4874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,multiply(X1,X2)))) = inverse(multiply(inverse(X3),X3)),
inference(superposition,[status(thm)],[c_123,c_4855]) ).
tcf(c_6813,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_4874,c_4874]) ).
tcf(c_6997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[c_6813,c_123]) ).
tcf(c_7011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2)) = X1,
inference(superposition,[status(thm)],[c_6813,c_123]) ).
tcf(c_7059,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_6997,c_7011]) ).
tcf(c_7074,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_7059]) ).
tcf(c_8807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_7011,c_2622]) ).
tcf(c_9392,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(demodulation,[status(thm)],[c_1346,c_7011]) ).
tcf(c_9401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),X4)))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_8807,c_9392]) ).
tcf(c_10194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),X4)) = multiply(inverse(multiply(X5,multiply(X1,X2))),multiply(X5,X4)),
inference(superposition,[status(thm)],[c_9401,c_7011]) ).
tcf(c_10813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,multiply(X1,X2))) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[c_7011,c_10194]) ).
tcf(c_12286,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_10813,c_10813]) ).
tcf(c_12547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(inverse(X2),X2)))))))),multiply(inverse(X3),X3))) = X1,
inference(superposition,[status(thm)],[c_12286,c_8807]) ).
tcf(c_16105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(multiply(X1,inverse(multiply(X4,inverse(multiply(inverse(X5),X5)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_218,c_7011]) ).
tcf(c_16161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_7011,c_2622]) ).
tcf(c_16180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(X5),X5)))))))),X1)) = X4,
inference(superposition,[status(thm)],[c_7011,c_16161]) ).
tcf(c_16346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2)) = multiply(inverse(multiply(X4,inverse(multiply(X1,inverse(multiply(X5,inverse(multiply(inverse(X6),X6)))))))),multiply(X4,X5)),
inference(superposition,[status(thm)],[c_16105,c_16105]) ).
tcf(c_16545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X3,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(X5),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(X6),X6))))))) = inverse(multiply(inverse(multiply(X7,X5)),multiply(X7,X1))),
inference(superposition,[status(thm)],[c_16180,c_16161]) ).
tcf(c_16675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2)))) = X1,
inference(superposition,[status(thm)],[c_16346,c_218]) ).
tcf(c_16830,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(demodulation,[status(thm)],[c_1346,c_7011]) ).
tcf(c_16840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),X4)))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_16161,c_16830]) ).
tcf(c_16843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X0),inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))))))),X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))) = multiply(inverse(X4),X4),
inference(superposition,[status(thm)],[c_12547,c_16830]) ).
tcf(c_16913,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_16843,c_16840]) ).
tcf(c_17506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))) = X1,
inference(superposition,[status(thm)],[c_16545,c_16180]) ).
tcf(c_18031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(inverse(X2),X2)))))))),multiply(inverse(X3),X3)))) = X1,
inference(superposition,[status(thm)],[c_16913,c_16675]) ).
tcf(c_18063,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(superposition,[status(thm)],[c_16913,c_17506]) ).
tcf(c_18471,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(inverse(multiply(inverse(X0),X0)))),inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(superposition,[status(thm)],[c_18063,c_18063]) ).
tcf(c_28264,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(X0,multiply(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[c_18471,c_18031]) ).
tcf(c_32662,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_7074]) ).
tcf(c_32663,negated_conjecture,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(renaming,[status(thm)],[c_32662]) ).
tcf(c_32664,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,multiply(X1,inverse(multiply(X1,multiply(inverse(X2),X2))))))) = X0,
inference(superposition,[status(thm)],[c_28264,c_28264]) ).
tcf(c_32695,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(inverse(X0),X0)))))))) = inverse(X1),
inference(superposition,[status(thm)],[c_51,c_28264]) ).
tcf(c_32723,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(inverse(X0),X0)))))))) = X1,
inference(superposition,[status(thm)],[c_32664,c_32695]) ).
tcf(c_32752,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),multiply(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[c_32723,c_51]) ).
tcf(c_32784,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(inverse(X0),X0))))))) = X1,
inference(superposition,[status(thm)],[c_32752,c_51]) ).
tcf(c_32785,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,multiply(inverse(X1),X1))) = multiply(inverse(X0),multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_32752,c_32752]) ).
tcf(c_33188,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X2),X2))))))) = X1,
inference(superposition,[status(thm)],[c_32785,c_32784]) ).
tcf(c_33193,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[c_32785,c_32752]) ).
tcf(c_33211,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(X0),inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2))))) = X0,
inference(superposition,[status(thm)],[c_32785,c_32752]) ).
tcf(c_33230,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(demodulation,[status(thm)],[c_33188,c_33193,c_33211]) ).
tcf(c_33466,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[c_32752,c_33230]) ).
tcf(c_33523,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(inverse(multiply(X0,inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_33230,c_32784]) ).
tcf(c_33525,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(inverse(multiply(X0,inverse(multiply(inverse(X0),X0))))))) = inverse(multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_33230,c_32723]) ).
tcf(c_33527,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_33230,c_32752]) ).
tcf(c_33532,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2)))))) = X0,
inference(superposition,[status(thm)],[c_33230,c_32664]) ).
tcf(c_33543,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(X1),X1))))) = X0,
inference(demodulation,[status(thm)],[c_33532,c_33230]) ).
tcf(c_33545,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_33523,c_33543]) ).
tcf(c_33547,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(X1),X1)),
inference(demodulation,[status(thm)],[c_33525,c_33543]) ).
tcf(c_33563,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[c_32663,c_33466]) ).
tcf(c_33753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),multiply(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_33545,c_51]) ).
tcf(c_33776,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),inverse(multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(inverse(X2),X2))))))) = X1,
inference(superposition,[status(thm)],[c_33545,c_32784]) ).
tcf(c_33900,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(multiply(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[c_33527,c_32752]) ).
tcf(c_34433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X4),X4))))))))),multiply(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_33547,c_33753]) ).
tcf(c_35304,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),X0))) = X1,
inference(superposition,[status(thm)],[c_33900,c_33776]) ).
tcf(c_35517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X3),X3))))))) = multiply(inverse(inverse(multiply(X0,X2))),X1),
inference(superposition,[status(thm)],[c_33753,c_35304]) ).
tcf(c_35550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X0)),inverse(multiply(inverse(X3),X3)))))))),X2)) = X1,
inference(superposition,[status(thm)],[c_35304,c_33753]) ).
tcf(c_35569,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(inverse(X0)),X1)),X0)) = X1,
inference(demodulation,[status(thm)],[c_35550,c_35304,c_35517]) ).
tcf(c_35817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(inverse(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))))),X2) = inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X0))),
inference(superposition,[status(thm)],[c_35569,c_33753]) ).
tcf(c_35822,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))))),X2) = multiply(inverse(X0),X2),
inference(superposition,[status(thm)],[c_35569,c_33776]) ).
tcf(c_35845,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),X1),
inference(light_normalisation,[status(thm)],[c_35817,c_35822]) ).
tcf(c_35919,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_33230,c_35845]) ).
tcf(c_36550,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_35304,c_35919]) ).
tcf(c_36634,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_28264,c_36550]) ).
tcf(c_36658,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_36634,c_36634]) ).
tcf(c_36677,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(demodulation,[status(thm)],[c_33193,c_36658]) ).
tcf(c_36706,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,multiply(X1,inverse(multiply(inverse(inverse(X1)),multiply(inverse(X2),X2))))))) = X0,
inference(superposition,[status(thm)],[c_36658,c_32664]) ).
tcf(c_36707,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,multiply(X1,inverse(multiply(X1,multiply(inverse(X2),X2))))))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_36658,c_32664]) ).
tcf(c_36712,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_36658,c_36634]) ).
tcf(c_36714,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_36706,c_36658,c_36707]) ).
tcf(c_37304,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(demodulation,[status(thm)],[c_34433,c_35919,c_36677,c_36714]) ).
tcf(c_37372,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_37304,c_36712]) ).
tcf(c_37401,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_33563,c_37372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP054-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 13:25:54 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 50.00/11.41 % SZS status Started for theBenchmark.p
% 50.00/11.41 % SZS status Unsatisfiable for theBenchmark.p
% 50.00/11.41
% 50.00/11.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.00/11.41
% 50.00/11.41 % ------ iProver source info
% 50.00/11.41
% 50.00/11.41 % git: date: 2026-07-19 20:42:38 +0200
% 50.00/11.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.00/11.41 % git: non_committed_changes: false
% 50.00/11.41
% 50.00/11.41 % ------ Parsing...% successful
% 50.00/11.41
% 50.00/11.41
% 50.00/11.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.00/11.41
% 50.00/11.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 50.00/11.41
% 50.00/11.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.00/11.41
% 50.00/11.41 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 50.00/11.41 % ------ Proving...
% 50.00/11.41 % ------ Problem Properties
% 50.00/11.41
% 50.00/11.41 %
% 50.00/11.41 % clauses 2
% 50.00/11.41 % conjectures 1
% 50.00/11.41 % EPR 0
% 50.00/11.41 % Horn 2
% 50.00/11.41 % unary 1
% 50.00/11.41 % binary 0
% 50.00/11.41 % lits 4
% 50.00/11.41 % lits eq 4
% 50.00/11.41 % fd_pure 0
% 50.00/11.41 % fd_pseudo 0
% 50.00/11.41 % fd_cond 0
% 50.00/11.41 % fd_pseudo_cond 0
% 50.00/11.41 % AC symbols 0
% 50.00/11.41
% 50.00/11.41 % ------ Input Options Time Limit: Unbounded
% 50.00/11.41
% 50.00/11.41
% 50.00/11.41 % ------
% 50.00/11.41 % Current options:
% 50.00/11.41 % ------
% 50.00/11.41
% 50.00/11.41
% 50.00/11.41 %
% 50.00/11.41
% 50.00/11.41 % ------ Proving...
% 50.00/11.41 %
% 50.00/11.41
% 50.00/11.41 % SZS status Unsatisfiable for theBenchmark.p
% 50.00/11.41
% 50.00/11.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.00/11.41
% 50.00/11.41
%------------------------------------------------------------------------------