%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:30:28 PM UTC 2026
% Result : Unsatisfiable 46.48s 13.38s
% Output : CNFRefutation 46.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of formulae : 52 ( 47 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 13 ( 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 : 155 ( 0 sgn 155 !; 0 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
file('/export/starexec/sandbox/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/sandbox/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,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_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
inference(cnf_transformation,[],[f1]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)))) = X4,
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = X2,
inference(superposition,[status(thm)],[c_108,c_52]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X2,multiply(X6,X8)))))),
inference(superposition,[status(thm)],[c_52,c_119]) ).
tcf(c_2375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))) = X3,
inference(superposition,[status(thm)],[c_144,c_119]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5))))) = X2,
inference(superposition,[status(thm)],[c_144,c_52]) ).
tcf(c_3022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(inverse(X4),X2))))),X3))) = X4,
inference(superposition,[status(thm)],[c_52,c_2375]) ).
tcf(c_3048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(X0,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(inverse(X2),multiply(inverse(X1),X5))))))))))) = X3,
inference(superposition,[status(thm)],[c_2375,c_2375]) ).
tcf(c_5401,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(inverse(X2),X1))))) = X2,
inference(superposition,[status(thm)],[c_2375,c_3048]) ).
tcf(c_6182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X3,multiply(X0,multiply(X1,multiply(X4,inverse(multiply(inverse(X2),X4))))))))))) = X3,
inference(superposition,[status(thm)],[c_5401,c_52]) ).
tcf(c_6269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),X2)))),inverse(X3)))) = X1,
inference(superposition,[status(thm)],[c_5401,c_5401]) ).
tcf(c_7912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3))) = X1,
inference(superposition,[status(thm)],[c_2393,c_6269]) ).
tcf(c_8120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)),inverse(X2)))) = X0,
inference(superposition,[status(thm)],[c_7912,c_2375]) ).
tcf(c_8129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)),inverse(X2)))) = X1,
inference(superposition,[status(thm)],[c_7912,c_5401]) ).
tcf(c_12419,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(X2,X1)))))) = X2,
inference(superposition,[status(thm)],[c_2375,c_6182]) ).
tcf(c_15018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)))) = X4,
inference(superposition,[status(thm)],[c_52,c_12419]) ).
tcf(c_15667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X4),X3))),X2)))),multiply(X4,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_5401,c_8120]) ).
tcf(c_25821,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_15667,c_7912]) ).
tcf(c_25830,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(inverse(X2),X2))))) = X0,
inference(superposition,[status(thm)],[c_15667,c_8120]) ).
tcf(c_25831,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(inverse(X2),X2))))) = X1,
inference(superposition,[status(thm)],[c_15667,c_8129]) ).
tcf(c_25835,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_15667,c_15018]) ).
tcf(c_25842,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_51,c_25821]) ).
tcf(c_39366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(X0,multiply(multiply(inverse(X1),X1),multiply(multiply(inverse(multiply(inverse(X2),X2)),X3),inverse(multiply(X4,multiply(X0,X3))))))) = X4,
inference(superposition,[status(thm)],[c_25835,c_52]) ).
tcf(c_40409,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2))) = X0,
inference(superposition,[status(thm)],[c_25821,c_25830]) ).
tcf(c_45844,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[c_25821,c_40409]) ).
tcf(c_46093,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[c_40409,c_40409]) ).
tcf(c_46095,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_25831,c_46093]) ).
tcf(c_46096,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[c_25830,c_46093]) ).
tcf(c_46103,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[c_12419,c_46095]) ).
tcf(c_48123,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(X0),multiply(X1,multiply(multiply(inverse(X1),X0),inverse(X2))))) = X2,
inference(superposition,[status(thm)],[c_45844,c_52]) ).
tcf(c_49273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(multiply(inverse(X0),multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(inverse(X4),X2))))),X3)) = multiply(inverse(X1),X4),
inference(superposition,[status(thm)],[c_3022,c_46095]) ).
tcf(c_49425,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_46095,c_45844]) ).
tcf(c_49441,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_3022,c_49273]) ).
tcf(c_50801,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_46096,c_48123]) ).
tcf(c_51546,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_46103,c_49425]) ).
tcf(c_51634,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),inverse(X1)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_46095,c_51546]) ).
tcf(c_51641,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_51546,c_46095]) ).
tcf(c_51642,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_51546,c_49441]) ).
tcf(c_51644,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(light_normalisation,[status(thm)],[c_51634,c_49425]) ).
tcf(c_51668,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c_49425,c_51644]) ).
tcf(c_51681,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[c_25821,c_51668]) ).
tcf(c_51694,plain,
( ( inverse(inverse(a2)) != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(demodulation,[status(thm)],[c_25842,c_51681]) ).
tcf(c_51695,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(ground_joinability,[status(thm)],[c_51694,c_49425]) ).
tcf(c_51914,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,multiply(X1,inverse(X2)))) = multiply(multiply(X2,inverse(X1)),inverse(X0)),
inference(superposition,[status(thm)],[c_51642,c_51641]) ).
tcf(c_51943,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(X0,multiply(X1,X2)),inverse(X2)),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[c_39366,c_49425,c_50801,c_51681,c_51914]) ).
tcf(c_51989,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X2)),inverse(X2)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_51943,c_51668]) ).
tcf(c_52234,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_51989,c_51668]) ).
tcf(c_52242,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_51695,c_52234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n006.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 13:25:35 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 46.48/13.38 % SZS status Started for theBenchmark.p
% 46.48/13.38 % SZS status Unsatisfiable for theBenchmark.p
% 46.48/13.38
% 46.48/13.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.48/13.38
% 46.48/13.38 % ------ iProver source info
% 46.48/13.38
% 46.48/13.38 % git: date: 2026-07-19 20:42:38 +0200
% 46.48/13.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.48/13.38 % git: non_committed_changes: false
% 46.48/13.38
% 46.48/13.38 % ------ Parsing...% successful
% 46.48/13.38
% 46.48/13.38
% 46.48/13.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.48/13.38
% 46.48/13.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 46.48/13.38
% 46.48/13.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.48/13.38
% 46.48/13.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 46.48/13.38 % ------ Proving...
% 46.48/13.38 % ------ Problem Properties
% 46.48/13.38
% 46.48/13.38 %
% 46.48/13.38 % clauses 2
% 46.48/13.38 % conjectures 1
% 46.48/13.38 % EPR 0
% 46.48/13.38 % Horn 2
% 46.48/13.38 % unary 1
% 46.48/13.38 % binary 0
% 46.48/13.38 % lits 4
% 46.48/13.38 % lits eq 4
% 46.48/13.38 % fd_pure 0
% 46.48/13.38 % fd_pseudo 0
% 46.48/13.38 % fd_cond 0
% 46.48/13.38 % fd_pseudo_cond 0
% 46.48/13.38 % AC symbols 0
% 46.48/13.38
% 46.48/13.38 % ------ Schedule dynamic 5 is on
% 46.48/13.38
% 46.48/13.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.48/13.38
% 46.48/13.38
% 46.48/13.38 % ------
% 46.48/13.38 % Current options:
% 46.48/13.38 % ------
% 46.48/13.38
% 46.48/13.38
% 46.48/13.38 %
% 46.48/13.38
% 46.48/13.38 % ------ Proving...
% 46.48/13.38 %
% 46.48/13.38
% 46.48/13.38 % SZS status Unsatisfiable for theBenchmark.p
% 46.48/13.38
% 46.48/13.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.48/13.38
% 46.48/13.38
%------------------------------------------------------------------------------