%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 01:33:40 PM UTC 2026
% Result : Unsatisfiable 40.14s 6.63s
% Output : CNFRefutation 40.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 9 ( 2 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 129 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = multiply(X0,inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X2,
inference(superposition,[status(thm)],[c_94,c_51]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[status(thm)],[c_94,c_51]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X2,
inference(superposition,[status(thm)],[c_133,c_133]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),inverse(multiply(X2,multiply(inverse(multiply(X0,X2)),multiply(inverse(multiply(X0,X2)),multiply(X0,X2)))))) = multiply(inverse(X1),multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_397,c_51]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_397,c_122]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(X0,X2)) = multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),X2)),
inference(superposition,[status(thm)],[c_397,c_445]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))))) = multiply(inverse(X1),X3),
inference(superposition,[status(thm)],[c_445,c_122]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[c_434,c_122]) ).
tcf(c_2593,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))) = inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))),
inference(superposition,[status(thm)],[c_681,c_397]) ).
tcf(c_6273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(X2),X2)))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[c_2593,c_2593]) ).
tcf(c_7080,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(X0,multiply(inverse(X1),multiply(inverse(X1),X1)))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_1236,c_631]) ).
tcf(c_8462,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_7080,c_7080]) ).
tcf(c_8755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X3),X3))))) = X2,
inference(superposition,[status(thm)],[c_8462,c_51]) ).
tcf(c_8788,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X1,
inference(superposition,[status(thm)],[c_8462,c_397]) ).
tcf(c_9808,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),multiply(inverse(X2),X2)))) = X1,
inference(superposition,[status(thm)],[c_8462,c_8788]) ).
tcf(c_10397,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_8462,c_9808]) ).
tcf(c_10466,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),multiply(inverse(X2),X2)))) = X1,
inference(superposition,[status(thm)],[c_9808,c_9808]) ).
tcf(c_10467,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(X2),X2)))) = X1,
inference(superposition,[status(thm)],[c_9808,c_6273]) ).
tcf(c_10581,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_10397,c_8462]) ).
tcf(c_10621,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X1)) = inverse(multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_10397,c_445]) ).
tcf(c_13742,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),X1)),multiply(inverse(X2),X2))) = X1,
inference(superposition,[status(thm)],[c_10581,c_10467]) ).
tcf(c_31407,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(inverse(X1),X1)) = inverse(multiply(X0,multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[c_10466,c_13742]) ).
tcf(c_34348,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(inverse(X0),X0),inverse(multiply(X1,multiply(inverse(X2),X2))))) = X1,
inference(superposition,[status(thm)],[c_31407,c_10466]) ).
tcf(c_34488,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(multiply(multiply(inverse(X0),X0),X1))),multiply(inverse(X2),X2)) = X1,
inference(superposition,[status(thm)],[c_31407,c_13742]) ).
tcf(c_36229,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))),X2)) = inverse(X2),
inference(superposition,[status(thm)],[c_8755,c_34348]) ).
tcf(c_38777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))),X2))),multiply(inverse(X3),X3)) = X2,
inference(superposition,[status(thm)],[c_31407,c_34488]) ).
tcf(c_38934,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)) = X0,
inference(light_normalisation,[status(thm)],[c_38777,c_36229]) ).
tcf(c_38936,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(demodulation,[status(thm)],[c_34488,c_38934]) ).
tcf(c_38944,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_10466,c_38936]) ).
tcf(c_40631,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[c_10621,c_38936]) ).
tcf(c_40692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(multiply(inverse(X0),X0),X1)),X2) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_38936,c_445]) ).
tcf(c_40720,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(X1),X2),
inference(light_normalisation,[status(thm)],[c_40692,c_38936]) ).
tcf(c_50423,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = multiply(X2,multiply(inverse(X2),X1)),
inference(superposition,[status(thm)],[c_38944,c_40720]) ).
tcf(c_50555,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_40720,c_38944]) ).
tcf(c_50558,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(light_normalisation,[status(thm)],[c_50423,c_40631]) ).
tcf(c_50670,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(inverse(X1),X2)) = multiply(X0,X2),
inference(superposition,[status(thm)],[c_40720,c_50558]) ).
tcf(c_50681,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X1)),X2) = multiply(inverse(X1),multiply(X0,X2)),
inference(superposition,[status(thm)],[c_50558,c_40720]) ).
tcf(c_50693,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(X0),X1),X2) = multiply(inverse(X0),multiply(X1,X2)),
inference(light_normalisation,[status(thm)],[c_50681,c_50555]) ).
tcf(c_50699,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_38936,c_50693]) ).
tcf(c_54439,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_50699,c_50670]) ).
tcf(c_54463,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_54439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:47:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running UEQ theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 40.14/6.63 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 40.14/6.63 % SZS status Started for theBenchmark.p
% 40.14/6.63 % SZS status Unsatisfiable for theBenchmark.p
% 40.14/6.63
% 40.14/6.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 40.14/6.63
% 40.14/6.63 % ------ iProver source info
% 40.14/6.63
% 40.14/6.63 % git: date: 2026-07-19 20:42:38 +0200
% 40.14/6.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 40.14/6.63 % git: non_committed_changes: false
% 40.14/6.63
% 40.14/6.63 % ------ Parsing...% successful
% 40.14/6.63
% 40.14/6.63
% 40.14/6.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 40.14/6.63
% 40.14/6.63 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 40.14/6.63
% 40.14/6.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 40.14/6.63
% 40.14/6.63 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 40.14/6.63 % ------ Proving...
% 40.14/6.63 % ------ Problem Properties
% 40.14/6.63
% 40.14/6.63 %
% 40.14/6.63 % clauses 2
% 40.14/6.63 % conjectures 1
% 40.14/6.63 % EPR 0
% 40.14/6.63 % Horn 2
% 40.14/6.63 % unary 2
% 40.14/6.63 % binary 0
% 40.14/6.63 % lits 2
% 40.14/6.63 % lits eq 2
% 40.14/6.63 % fd_pure 0
% 40.14/6.63 % fd_pseudo 0
% 40.14/6.63 % fd_cond 0
% 40.14/6.63 % fd_pseudo_cond 0
% 40.14/6.63 % AC symbols 0
% 40.14/6.63
% 40.14/6.63 % ------ Input Options Time Limit: Unbounded
% 40.14/6.63
% 40.14/6.63
% 40.14/6.63 % ------
% 40.14/6.63 % Current options:
% 40.14/6.63 % ------
% 40.14/6.63
% 40.14/6.63
% 40.14/6.63 %
% 40.14/6.63
% 40.14/6.63 % ------ Proving...
% 40.14/6.63 %
% 40.14/6.63
% 40.14/6.63 % SZS status Unsatisfiable for theBenchmark.p
% 40.14/6.63
% 40.14/6.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 40.14/6.64
% 40.14/6.64
%------------------------------------------------------------------------------