%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG008-7 : 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 02:38:10 PM UTC 2026
% Result : Unsatisfiable 3.24s 1.19s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_identity) ).
fof(f5,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).
fof(f6,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).
fof(f8,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
fof(f10,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).
fof(f11,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).
fof(f12,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
fof(f13,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f14,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f15,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f14]) ).
tcf(c_61,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_71,negated_conjecture,
multiply(a,b) = c,
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,negated_conjecture,
multiply(b,a) != c,
inference(cnf_transformation,[],[f15]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_65,c_64]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_70,c_68]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_70,c_68]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_70,c_69]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(multiply(X0,X1),X1),
inference(superposition,[status(thm)],[c_70,c_69]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_104,c_61]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(X1,multiply(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_140,c_65,c_66]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_126,c_65,c_66]) ).
tcf(c_264,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_64,c_151]) ).
tcf(c_348,plain,
! [X0: $i] : add(X0,multiply(X0,additive_identity)) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_62,c_123]) ).
tcf(c_349,plain,
! [X0: $i] : add(X0,multiply(X0,additive_inverse(X0))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_64,c_123]) ).
tcf(c_387,plain,
! [X0: $i] : add(X0,multiply(additive_inverse(X0),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_64,c_137]) ).
tcf(c_475,plain,
! [X0: $i] : add(X0,multiply(additive_identity,X0)) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_61,c_153]) ).
tcf(c_514,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_264,c_62]) ).
tcf(c_516,plain,
! [X0: $i] : add(X0,multiply(additive_identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_475,c_70]) ).
tcf(c_518,plain,
! [X0: $i] : add(X0,multiply(X0,additive_identity)) = X0,
inference(demodulation,[status(thm)],[c_348,c_70]) ).
tcf(c_1178,plain,
! [X0: $i] : add(X0,add(multiply(additive_identity,X0),additive_inverse(X0))) = additive_identity,
inference(superposition,[status(thm)],[c_516,c_106]) ).
tcf(c_1183,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = multiply(additive_identity,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_516,c_151]) ).
tcf(c_1206,plain,
! [X0: $i] : add(X0,add(multiply(X0,additive_identity),additive_inverse(X0))) = additive_identity,
inference(superposition,[status(thm)],[c_518,c_106]) ).
tcf(c_1211,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = multiply(additive_inverse(X0),additive_identity),
inference(superposition,[status(thm)],[c_518,c_151]) ).
tcf(c_1310,plain,
! [X0: $i] : add(X0,add(multiply(X0,additive_inverse(X0)),additive_inverse(multiply(X0,additive_identity)))) = additive_identity,
inference(superposition,[status(thm)],[c_349,c_106]) ).
tcf(c_1314,plain,
! [X0: $i] : multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))) = add(X0,multiply(additive_inverse(X0),additive_identity)),
inference(superposition,[status(thm)],[c_349,c_151]) ).
tcf(c_1335,plain,
! [X0: $i,X1: $i] : add(X0,add(multiply(additive_inverse(X0),X0),X1)) = add(multiply(additive_identity,X0),X1),
inference(superposition,[status(thm)],[c_387,c_65]) ).
tcf(c_1338,plain,
! [X0: $i] : multiply(additive_inverse(additive_inverse(X0)),additive_inverse(X0)) = add(X0,multiply(additive_identity,additive_inverse(X0))),
inference(superposition,[status(thm)],[c_387,c_151]) ).
tcf(c_1426,plain,
! [X0: $i] : multiply(additive_inverse(X0),additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_1211,c_64]) ).
tcf(c_1427,plain,
! [X0: $i] : multiply(additive_identity,additive_inverse(X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_1183,c_64]) ).
tcf(c_1432,plain,
! [X0: $i] : add(X0,add(additive_inverse(X0),multiply(X0,additive_identity))) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_1206,c_65,c_66]) ).
tcf(c_1433,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_1432,c_151]) ).
tcf(c_1436,plain,
! [X0: $i] : add(X0,add(additive_inverse(X0),multiply(additive_identity,X0))) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_1178,c_65,c_66]) ).
tcf(c_1437,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_1436,c_151]) ).
tcf(c_1525,plain,
! [X0: $i] : multiply(additive_inverse(additive_inverse(X0)),additive_inverse(X0)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_1338,c_1427]) ).
tcf(c_1526,plain,
! [X0: $i] : multiply(X0,additive_inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_1525,c_62,c_514]) ).
tcf(c_1536,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(X0),
inference(demodulation,[status(thm)],[c_1314,c_1426,c_1526]) ).
tcf(c_1537,plain,
! [X0: $i] : additive_inverse(X0) = X0,
inference(demodulation,[status(thm)],[c_1536,c_62]) ).
tcf(c_1538,plain,
! [X0: $i] : add(X0,add(X0,additive_identity)) = additive_identity,
inference(demodulation,[status(thm)],[c_1310,c_1433,c_1526,c_1537]) ).
tcf(c_1539,plain,
! [X0: $i] : add(X0,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_1538,c_62]) ).
tcf(c_1602,plain,
! [X0: $i,X1: $i] : add(X0,add(multiply(X0,X0),X1)) = add(additive_identity,X1),
inference(demodulation,[status(thm)],[c_1335,c_1437,c_1537]) ).
tcf(c_1603,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1602,c_70,c_61]) ).
tcf(c_3248,plain,
! [X0: $i,X1: $i] : add(add(X0,X1),multiply(X0,add(X0,X1))) = multiply(X1,add(X0,X1)),
inference(superposition,[status(thm)],[c_1603,c_153]) ).
tcf(c_3586,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,multiply(X0,add(X0,X1)))) = multiply(X1,add(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_3248,c_65,c_66]) ).
tcf(c_3587,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,add(X0,multiply(X0,X1)))) = add(X1,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_3586,c_123,c_155]) ).
tcf(c_3588,plain,
! [X0: $i,X1: $i] : add(X0,add(multiply(X1,X0),additive_identity)) = add(X0,multiply(X0,X1)),
inference(ac_demodulation,[status(thm)],[c_3587,c_1539,c_65,c_66]) ).
tcf(c_3589,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = add(X0,multiply(X1,X0)),
inference(ac_demodulation,[status(thm)],[c_3588,c_61,c_65,c_66]) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,multiply(X0,X1))) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_3589,c_1603]) ).
tcf(c_4091,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_3827,c_1603]) ).
tcf(c_4472,plain,
multiply(a,b) != c,
inference(demodulation,[status(thm)],[c_72,c_4091]) ).
tcf(c_4492,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4472,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n006.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:43:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running UEQ theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 3.24/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.24/1.19 % SZS status Started for theBenchmark.p
% 3.24/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.19
% 3.24/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.24/1.19
% 3.24/1.19 % ------ iProver source info
% 3.24/1.19
% 3.24/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.24/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.24/1.19 % git: non_committed_changes: false
% 3.24/1.19
% 3.24/1.19 % ------ Parsing...% successful
% 3.24/1.19
% 3.24/1.19
% 3.24/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.24/1.19 % ------ Proving...
% 3.24/1.19 % ------ Problem Properties
% 3.24/1.19
% 3.24/1.19 %
% 3.24/1.19 % clauses 12
% 3.24/1.19 % conjectures 2
% 3.24/1.19 % EPR 0
% 3.24/1.19 % Horn 12
% 3.24/1.19 % unary 12
% 3.24/1.19 % binary 0
% 3.24/1.19 % lits 12
% 3.24/1.19 % lits eq 12
% 3.24/1.19 % fd_pure 0
% 3.24/1.19 % fd_pseudo 0
% 3.24/1.19 % fd_cond 0
% 3.24/1.19 % fd_pseudo_cond 0
% 3.24/1.19 % AC symbols 1
% 3.24/1.19
% 3.24/1.19 % ------ Input Options Time Limit: Unbounded
% 3.24/1.19
% 3.24/1.19
% 3.24/1.19 % ------
% 3.24/1.19 % Current options:
% 3.24/1.19 % ------
% 3.24/1.19
% 3.24/1.19
% 3.24/1.19 %
% 3.24/1.19
% 3.24/1.19 % ------ Proving...
% 3.24/1.19 %
% 3.24/1.19
% 3.24/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.19
% 3.24/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.24/1.19
% 3.24/1.19
%------------------------------------------------------------------------------