%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 01:30:42 PM UTC 2026
% Result : Unsatisfiable 4.17s 1.28s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 25 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| 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(a4,b4) != multiply(b4,a4)
| 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(a4,b4) != multiply(b4,a4) )
| ( 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] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X3,X2))))))) = X3,
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_52,c_113]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_117,c_113]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(multiply(X1,multiply(X2,inverse(X0))),inverse(X2))) = X1,
inference(superposition,[status(thm)],[c_144,c_52]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X2,X1)))) = X0,
inference(superposition,[status(thm)],[c_144,c_113]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X3,inverse(multiply(X3,X1)))),inverse(X0))) = X2,
inference(superposition,[status(thm)],[c_165,c_52]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(X2,inverse(X0))) = multiply(X2,X1),
inference(superposition,[status(thm)],[c_165,c_113]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(multiply(X1,X2),inverse(X1))) = multiply(X0,X2),
inference(superposition,[status(thm)],[c_190,c_163]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[c_304,c_190]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(multiply(X1,inverse(X0)),X2)) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_359,c_144]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_429,c_117]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_429,c_304]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c_479,c_144]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[c_501,c_359]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[c_519,c_429]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_519,c_144]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(X1)))) = multiply(X2,X0),
inference(demodulation,[status(thm)],[c_190,c_533]) ).
tcf(c_541,plain,
( ( multiply(a4,b4) != multiply(b4,a4) )
| ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(b2,multiply(inverse(b2),a2)) != a2 ) ),
inference(demodulation,[status(thm)],[c_51,c_533]) ).
tcf(c_542,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(b2,multiply(inverse(b2),a2)) != a2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_541,c_534]) ).
tcf(c_594,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(ground_joinability,[status(thm)],[c_542,c_144,c_534]) ).
tcf(c_595,plain,
( ( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) )
| ( multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(a3,c3)) ) ),
inference(demodulation,[status(thm)],[c_594,c_533,c_534]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_534,c_144]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X2,X1))) = X2,
inference(demodulation,[status(thm)],[c_188,c_533,c_540]) ).
tcf(c_707,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[c_674,c_613]) ).
tcf(c_799,plain,
multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(a3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[c_595,c_483]) ).
tcf(c_1696,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[c_707,c_534]) ).
tcf(c_1701,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_799,c_1696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:31:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.17/1.28 % SZS status Started for theBenchmark.p
% 4.17/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/1.28
% 4.17/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.17/1.28
% 4.17/1.28 % ------ iProver source info
% 4.17/1.28
% 4.17/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.17/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.17/1.28 % git: non_committed_changes: false
% 4.17/1.28
% 4.17/1.28 % ------ Parsing...% successful
% 4.17/1.28
% 4.17/1.28
% 4.17/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.17/1.28
% 4.17/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.17/1.28
% 4.17/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.17/1.28
% 4.17/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.17/1.28 % ------ Proving...
% 4.17/1.28 % ------ Problem Properties
% 4.17/1.28
% 4.17/1.28 %
% 4.17/1.28 % clauses 2
% 4.17/1.28 % conjectures 1
% 4.17/1.28 % EPR 0
% 4.17/1.28 % Horn 2
% 4.17/1.28 % unary 1
% 4.17/1.28 % binary 0
% 4.17/1.28 % lits 5
% 4.17/1.28 % lits eq 5
% 4.17/1.28 % fd_pure 0
% 4.17/1.28 % fd_pseudo 0
% 4.17/1.28 % fd_cond 0
% 4.17/1.28 % fd_pseudo_cond 0
% 4.17/1.28 % AC symbols 0
% 4.17/1.28
% 4.17/1.28 % ------ Schedule dynamic 5 is on
% 4.17/1.28
% 4.17/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.17/1.28
% 4.17/1.28
% 4.17/1.28 % ------
% 4.17/1.28 % Current options:
% 4.17/1.28 % ------
% 4.17/1.28
% 4.17/1.28
% 4.17/1.28 %
% 4.17/1.28
% 4.17/1.28 % ------ Proving...
% 4.17/1.28 %
% 4.17/1.28
% 4.17/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/1.28
% 4.17/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.17/1.28
% 4.17/1.28
%------------------------------------------------------------------------------